Anxiety Training Efficacy and Mechanisms

Note

This document is designed to be used with a project folder with three sub-folders: “data” (containing “at_data.csv”), “scripts”, and “output”.

Load packages

library(tidyverse)
library(here)
library(skimr)
library(janitor)
library(afex)
library(ggplot2)
library(rstatix)
library(effsize)
library(vtable)
library(apaTables)

Load data

at <- read_csv(here("data","at_data.csv"))

Identify and remove outliers

Calculate z-scores for post-tests

at$z.re_lp = (at$re_lp - mean(at$re_lp)) / sd(at$re_lp)
at$z.re_mp = (at$re_mp - mean(at$re_mp)) / sd(at$re_mp)
at$z.re_hp = (at$re_hp - mean(at$re_hp)) / sd(at$re_hp)

Remove participants with z-scores > 3.00 or < -3.00

at_no.outliers <- at %>% filter(at$z.re_lp <= 3 & at$z.re_lp >= -3 & at$z.re_mp <= 3 & at$z.re_mp >= -3 & at$z.re_hp <= 3 & at$z.re_hp >= -3)

Consistency analyses

Cognitive anxiety

Pre-test

Cronbach::cronbach(subset(at_no.outliers, select = c(cog.anx.01_pre, cog.anx.02_pre, cog.anx.03_pre, cog.anx.04_pre, cog.anx.05_pre)))

## [1] 0.7490524

Day 1

Cronbach::cronbach(subset(at_no.outliers, select = c(cog.anx.01_d01, cog.anx.02_d01, cog.anx.03_d01, cog.anx.04_d01, cog.anx.05_d01)))

## [1] 0.8044323

Day 2

Cronbach::cronbach(subset(at_no.outliers, select = c(cog.anx.01_d02, cog.anx.02_d02, cog.anx.03_d02, cog.anx.04_d02, cog.anx.05_d02)))

## [1] 0.831078

Low-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(cog.anx.01_lp, cog.anx.02_lp, cog.anx.03_lp, cog.anx.04_lp, cog.anx.05_lp)))

## [1] 0.8228548

Mild-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(cog.anx.01_mp, cog.anx.02_mp, cog.anx.03_mp, cog.anx.04_mp, cog.anx.05_mp)))

## [1] 0.8664285

High-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(cog.anx.01_hp, cog.anx.02_hp, cog.anx.03_hp, cog.anx.04_hp, cog.anx.05_hp)))

## [1] 0.8676775

Somatic anxiety

Pre-test

Cronbach::cronbach(subset(at_no.outliers, select = c(som.anx.01_pre, som.anx.02_pre, som.anx.03_pre, som.anx.04_pre, som.anx.05_pre, som.anx.06_pre, som.anx.07_pre)))

## [1] 0.6503218

Day 1

Cronbach::cronbach(subset(at_no.outliers, select = c(som.anx.01_d01, som.anx.02_d01, som.anx.03_d01, som.anx.04_d01, som.anx.05_d01, som.anx.06_d01, som.anx.07_d01)))

## [1] 0.7792101

Day 2

Cronbach::cronbach(subset(at_no.outliers, select = c(som.anx.01_d02, som.anx.02_d02, som.anx.03_d02, som.anx.04_d02, som.anx.05_d02, som.anx.06_d02, som.anx.07_d02)))

## [1] 0.7636387

Low-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(som.anx.01_lp, som.anx.02_lp, som.anx.03_lp, som.anx.04_lp, som.anx.05_lp, som.anx.06_lp, som.anx.07_lp)))

## [1] 0.7076106

Mild-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(som.anx.01_mp, som.anx.02_mp, som.anx.03_mp, som.anx.04_mp, som.anx.05_mp, som.anx.06_mp, som.anx.07_mp)))

## [1] 0.8362272

High-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(som.anx.01_hp, som.anx.02_hp, som.anx.03_hp, som.anx.04_hp, som.anx.05_hp, som.anx.06_hp, som.anx.07_hp)))

## [1] 0.8361927

Self-confidence

Pre-test

Cronbach::cronbach(subset(at_no.outliers, select = c(sc.01_pre, sc.02_pre, sc.03_pre, sc.04_pre, sc.05_pre)))

## [1] 0.8149773

Day 1

Cronbach::cronbach(subset(at_no.outliers, select = c(sc.01_d01, sc.02_d01, sc.03_d01, sc.04_d01, sc.05_d01)))

## [1] 0.8755821

Day 2

Cronbach::cronbach(subset(at_no.outliers, select = c(sc.01_d02, sc.02_d02, sc.03_d02, sc.04_d02, sc.05_d02)))

## [1] 0.8678035

Low-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(sc.01_lp, sc.02_lp, sc.03_lp, sc.04_lp, sc.05_lp)))

## [1] 0.8944913

Mild-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(sc.01_mp, sc.02_mp, sc.03_mp, sc.04_mp, sc.05_mp)))

## [1] 0.9017425

High-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(sc.01_hp, sc.02_hp, sc.03_hp, sc.04_hp, sc.05_hp)))

## [1] 0.9122342

Movement reinvestment

Pre-test

Cronbach::cronbach(subset(at_no.outliers, select = c(rein.01_pre, rein.02_pre, rein.03_pre, rein.04_pre, rein.05_pre)))

## [1] 0.672492

Day 1

Cronbach::cronbach(subset(at_no.outliers, select = c(rein.01_d01, rein.02_d01, rein.03_d01, rein.04_d01, rein.05_d01)))

## [1] 0.7595312

Day 2

Cronbach::cronbach(subset(at_no.outliers, select = c(rein.01_d02, rein.02_d02, rein.03_d02, rein.04_d02, rein.05_d02)))

## [1] 0.7964137

Low-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(rein.01_lp, rein.02_lp, rein.03_lp, rein.04_lp, rein.05_lp)))

## [1] 0.8900579

Mild-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(rein.01_mp, rein.02_mp, rein.03_mp, rein.04_mp, rein.05_mp)))

## [1] 0.8332471

High-pressure post-test

Cronbach::cronbach(subset(at_no.outliers, select = c(rein.01_hp, rein.02_hp, rein.03_hp, rein.04_hp, rein.05_hp)))

## [1] 0.8278967

Average cognitive anxiety items for each time point

at_no.outliers$cog.anx_pre = ((at_no.outliers$cog.anx.01_pre + at_no.outliers$cog.anx.02_pre + at_no.outliers$cog.anx.03_pre + at_no.outliers$cog.anx.04_pre + at_no.outliers$cog.anx.05_pre) / 5)

at_no.outliers$cog.anx_d01 = ((at_no.outliers$cog.anx.01_d01 + at_no.outliers$cog.anx.02_d01 + at_no.outliers$cog.anx.03_d01 + at_no.outliers$cog.anx.04_d01 + at_no.outliers$cog.anx.05_d01) / 5)

at_no.outliers$cog.anx_d02 = ((at_no.outliers$cog.anx.01_d02 + at_no.outliers$cog.anx.02_d02 + at_no.outliers$cog.anx.03_d02 + at_no.outliers$cog.anx.04_d02 + at_no.outliers$cog.anx.05_d02) / 5)

at_no.outliers$cog.anx_lp = ((at_no.outliers$cog.anx.01_lp + at_no.outliers$cog.anx.02_lp + at_no.outliers$cog.anx.03_lp + at_no.outliers$cog.anx.04_lp + at_no.outliers$cog.anx.05_lp) / 5)

at_no.outliers$cog.anx_mp = ((at_no.outliers$cog.anx.01_mp + at_no.outliers$cog.anx.02_mp + at_no.outliers$cog.anx.03_mp + at_no.outliers$cog.anx.04_mp + at_no.outliers$cog.anx.05_mp) / 5)

at_no.outliers$cog.anx_hp = ((at_no.outliers$cog.anx.01_hp + at_no.outliers$cog.anx.02_hp + at_no.outliers$cog.anx.03_hp + at_no.outliers$cog.anx.04_hp + at_no.outliers$cog.anx.05_hp) / 5)

Average somatic anxiety items for each time point

at_no.outliers$som.anx_pre = ((at_no.outliers$som.anx.01_pre + at_no.outliers$som.anx.02_pre + at_no.outliers$som.anx.03_pre + at_no.outliers$som.anx.04_pre + at_no.outliers$som.anx.05_pre + at_no.outliers$som.anx.06_pre + at_no.outliers$som.anx.07_pre) / 7)

at_no.outliers$som.anx_d01 = ((at_no.outliers$som.anx.01_d01 + at_no.outliers$som.anx.02_d01 + at_no.outliers$som.anx.03_d01 + at_no.outliers$som.anx.04_d01 + at_no.outliers$som.anx.05_d01 + at_no.outliers$som.anx.06_d01 + at_no.outliers$som.anx.07_d01) / 7)

at_no.outliers$som.anx_d02 = ((at_no.outliers$som.anx.01_d02 + at_no.outliers$som.anx.02_d02 + at_no.outliers$som.anx.03_d02 + at_no.outliers$som.anx.04_d02 + at_no.outliers$som.anx.05_d02 + at_no.outliers$som.anx.06_d02 + at_no.outliers$som.anx.07_d02) / 7)

at_no.outliers$som.anx_lp = ((at_no.outliers$som.anx.01_lp + at_no.outliers$som.anx.02_lp + at_no.outliers$som.anx.03_lp + at_no.outliers$som.anx.04_lp + at_no.outliers$som.anx.05_lp + at_no.outliers$som.anx.06_lp + at_no.outliers$som.anx.07_lp) / 7)

at_no.outliers$som.anx_mp = ((at_no.outliers$som.anx.01_mp + at_no.outliers$som.anx.02_mp + at_no.outliers$som.anx.03_mp + at_no.outliers$som.anx.04_mp + at_no.outliers$som.anx.05_mp + at_no.outliers$som.anx.06_mp + at_no.outliers$som.anx.07_mp) / 7)

at_no.outliers$som.anx_hp = ((at_no.outliers$som.anx.01_hp + at_no.outliers$som.anx.02_hp + at_no.outliers$som.anx.03_hp + at_no.outliers$som.anx.04_hp + at_no.outliers$som.anx.05_hp + at_no.outliers$som.anx.06_hp + at_no.outliers$som.anx.07_hp) / 7)

Average self-confidence items for each time point

at_no.outliers$sc_pre = ((at_no.outliers$sc.01_pre + at_no.outliers$sc.02_pre + at_no.outliers$sc.03_pre + at_no.outliers$sc.04_pre + at_no.outliers$sc.05_pre) / 5)

at_no.outliers$sc_d01 = ((at_no.outliers$sc.01_d01 + at_no.outliers$sc.02_d01 + at_no.outliers$sc.03_d01 + at_no.outliers$sc.04_d01 + at_no.outliers$sc.05_d01) / 5)

at_no.outliers$sc_d02 = ((at_no.outliers$sc.01_d02 + at_no.outliers$sc.02_d02 + at_no.outliers$sc.03_d02 + at_no.outliers$sc.04_d02 + at_no.outliers$sc.05_d02) / 5)

at_no.outliers$sc_lp = ((at_no.outliers$sc.01_lp + at_no.outliers$sc.02_lp + at_no.outliers$sc.03_lp + at_no.outliers$sc.04_lp + at_no.outliers$sc.05_lp) / 5)

at_no.outliers$sc_mp = ((at_no.outliers$sc.01_mp + at_no.outliers$sc.02_mp + at_no.outliers$sc.03_mp + at_no.outliers$sc.04_mp + at_no.outliers$sc.05_mp) / 5)

at_no.outliers$sc_hp = ((at_no.outliers$sc.01_hp + at_no.outliers$sc.02_hp + at_no.outliers$sc.03_hp + at_no.outliers$sc.04_hp + at_no.outliers$sc.05_hp) / 5)

Average movement reinvestment items for each time point

at_no.outliers$rein_pre = ((at_no.outliers$rein.01_pre + at_no.outliers$rein.02_pre + at_no.outliers$rein.03_pre + at_no.outliers$rein.04_pre + at_no.outliers$rein.05_pre + at_no.outliers$rein.06_pre) / 6)

at_no.outliers$rein_d01 = ((at_no.outliers$rein.01_d01 + at_no.outliers$rein.02_d01 + at_no.outliers$rein.03_d01 + at_no.outliers$rein.04_d01 + at_no.outliers$rein.05_d01 + at_no.outliers$rein.06_d01) / 6)

at_no.outliers$rein_d02 = ((at_no.outliers$rein.01_d02 + at_no.outliers$rein.02_d02 + at_no.outliers$rein.03_d02 + at_no.outliers$rein.04_d02 + at_no.outliers$rein.05_d02 + at_no.outliers$rein.06_d02) / 6)

at_no.outliers$rein_lp = ((at_no.outliers$rein.01_lp + at_no.outliers$rein.02_lp + at_no.outliers$rein.03_lp + at_no.outliers$rein.04_lp + at_no.outliers$rein.05_lp + at_no.outliers$rein.06_lp) / 6)

at_no.outliers$rein_mp = ((at_no.outliers$rein.01_mp + at_no.outliers$rein.02_mp + at_no.outliers$rein.03_mp + at_no.outliers$rein.04_mp + at_no.outliers$rein.05_mp + at_no.outliers$rein.06_mp) / 6)

at_no.outliers$rein_hp = ((at_no.outliers$rein.01_hp + at_no.outliers$rein.02_hp + at_no.outliers$rein.03_hp + at_no.outliers$rein.04_hp + at_no.outliers$rein.05_hp + at_no.outliers$rein.06_hp) / 6)

Calculate challenge-threat score for each time point

at_no.outliers$ct_pre = (at_no.outliers$challenge_pre / at_no.outliers$threat_pre)

at_no.outliers$ct_d01 = (at_no.outliers$challenge_d01 / at_no.outliers$threat_d01)

at_no.outliers$ct_d02 = (at_no.outliers$challenge_d02 / at_no.outliers$threat_d02)

at_no.outliers$ct_lp = (at_no.outliers$challenge_lp / at_no.outliers$threat_lp)

at_no.outliers$ct_mp = (at_no.outliers$challenge_mp / at_no.outliers$threat_mp)

at_no.outliers$ct_hp = (at_no.outliers$challenge_hp / at_no.outliers$threat_hp)

Identify participants who did not follow pre-experiment instructions for Day 3

Calculate difference in sleep on night before Day 3 from average of nights before Days 1 and 2

at_no.outliers$sleep_diff = abs(((at_no.outliers$sleep_d01 + at_no.outliers$sleep_d02) / 2) - at_no.outliers$sleep_d03)

Remove participants who did not follow pre-experiment instructions for Day 3

at_fail.instruct <- at_no.outliers %>% filter(at_no.outliers$sleep_diff <= 2 & at_no.outliers$alc_d03 == 0 & at_no.outliers$caff_d03 == 0)

Correlations between cognitive and somatic anxiety subscales at each time point

cor(at_no.outliers$som.anx_pre,at_no.outliers$cog.anx_pre)

## [1] 0.3252593

cor(at_no.outliers$som.anx_d01,at_no.outliers$cog.anx_d01)

## [1] 0.4000744

cor(at_no.outliers$som.anx_d02,at_no.outliers$cog.anx_d02)

## [1] 0.417241

cor(at_no.outliers$som.anx_lp,at_no.outliers$cog.anx_lp)

## [1] 0.4047639

cor(at_no.outliers$som.anx_mp,at_no.outliers$cog.anx_mp)

## [1] 0.4651393

cor(at_no.outliers$som.anx_hp,at_no.outliers$cog.anx_hp)

## [1] 0.4384734

Since subscales were not strongly correlated, they were not averaged together.

Data normality assessment and transformation (based on post-tests)

Radial error

Q-Q plots for radial error

qqnorm(at_no.outliers$re_lp, datax = T, main = "Low-Pressure Post-Test Radial Error")

qqnorm(at_no.outliers$re_mp, datax = T, main = "Mild-Pressure Post-Test Radial Error")

qqnorm(at_no.outliers$re_hp, datax = T, main = "High-Pressure Post-Test Radial Error")

Shapiro-Wilk tests for radial error

shapiro.test(at_no.outliers$re_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$re_lp
## W = 0.96638, p-value = 0.03345

shapiro.test(at_no.outliers$re_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$re_mp
## W = 0.95797, p-value = 0.01013

shapiro.test(at_no.outliers$re_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$re_hp
## W = 0.96718, p-value = 0.03759

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that radial error data were normally distributed.

Cognitive anxiety

Q-Q plots for cognitive anxiety

qqnorm(at_no.outliers$cog.anx_lp, datax = T, main = "Low-Pressure Post-Test Cognitive Anxiety")

qqnorm(at_no.outliers$cog.anx_mp, datax = T, main = "Mild-Pressure Post-Test Cognitive Anxiety")

qqnorm(at_no.outliers$cog.anx_hp, datax = T, main = "High-Pressure Post-Test Cognitive Anxiety")

Shapiro-Wilk tests for cognitive anxiety

shapiro.test(at_no.outliers$cog.anx_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$cog.anx_lp
## W = 0.90602, p-value = 2.207e-05

shapiro.test(at_no.outliers$cog.anx_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$cog.anx_mp
## W = 0.93987, p-value = 0.0009481

shapiro.test(at_no.outliers$cog.anx_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$cog.anx_hp
## W = 0.96721, p-value = 0.03774

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that cognitive anxiety data were non-normally distributed. Thus, two transformations, a log transformation and a reverse log transformation, were attempted to normalize it.

Log and reverse log transformations of cognitive anxiety data

at_no.outliers$ln.cog.anx_lp = log(at_no.outliers$cog.anx_lp)
at_no.outliers$ln.cog.anx_mp = log(at_no.outliers$cog.anx_mp)
at_no.outliers$ln.cog.anx_hp = log(at_no.outliers$cog.anx_hp)
at_no.outliers$rln.cog.anx_lp = log((max(at_no.outliers$cog.anx_lp+1)-at_no.outliers$cog.anx_lp))
at_no.outliers$rln.cog.anx_mp = log((max(at_no.outliers$cog.anx_mp+1)-at_no.outliers$cog.anx_mp))
at_no.outliers$rln.cog.anx_hp = log((max(at_no.outliers$cog.anx_hp+1)-at_no.outliers$cog.anx_hp))

Q-Q plots of log and reverse log transformed cognitive anxiety data

qqnorm(at_no.outliers$ln.cog.anx_lp, datax = T, main = "Low-Pressure Post-Test Cognitive Anxiety (log)")

qqnorm(at_no.outliers$ln.cog.anx_mp, datax = T, main = "Mild-Pressure Post-Test Cognitive Anxiety (log)")

qqnorm(at_no.outliers$ln.cog.anx_hp, datax = T, main = "High-Pressure Post-Test Cognitive Anxiety (log)")

qqnorm(at_no.outliers$rln.cog.anx_lp, datax = T, main = "Low-Pressure Post-Test 
Reverse Cognitive Anxiety (log)")

qqnorm(at_no.outliers$rln.cog.anx_mp, datax = T, main = "Mild-Pressure Post-Test Reverse Cognitive Anxiety (log)")

qqnorm(at_no.outliers$rln.cog.anx_hp, datax = T, main = "High-Pressure Post-Test Reverse Cognitive Anxiety (log)")

Shapiro-Wilk tests of log and reverse log transformed cognitive anxiety data

shapiro.test(at_no.outliers$ln.cog.anx_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.cog.anx_lp
## W = 0.915, p-value = 5.565e-05

shapiro.test(at_no.outliers$ln.cog.anx_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.cog.anx_mp
## W = 0.96635, p-value = 0.0333

shapiro.test(at_no.outliers$ln.cog.anx_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.cog.anx_hp
## W = 0.95793, p-value = 0.01007

shapiro.test(at_no.outliers$rln.cog.anx_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.cog.anx_lp
## W = 0.86884, p-value = 7.357e-07

shapiro.test(at_no.outliers$rln.cog.anx_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.cog.anx_mp
## W = 0.85561, p-value = 2.509e-07

shapiro.test(at_no.outliers$rln.cog.anx_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.cog.anx_hp
## W = 0.93284, p-value = 0.0004062

Somatic anxiety

Q-Q plots for somatic anxiety

qqnorm(at_no.outliers$som.anx_lp, datax = T, main = "Low-Pressure Post-Test Somatic Anxiety")

qqnorm(at_no.outliers$som.anx_mp, datax = T, main = "Mild-Pressure Post-Test Somatic Anxiety")

qqnorm(at_no.outliers$som.anx_hp, datax = T, main = "High-Pressure Post-Test Somatic Anxiety")

Shapiro-Wilk tests for cognitive anxiety

shapiro.test(at_no.outliers$som.anx_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$som.anx_lp
## W = 0.6475, p-value = 1.463e-12

shapiro.test(at_no.outliers$som.anx_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$som.anx_mp
## W = 0.73507, p-value = 1.039e-10

shapiro.test(at_no.outliers$som.anx_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$som.anx_hp
## W = 0.86798, p-value = 6.852e-07

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that somatic anxiety data were non-normally distributed. Thus, two transformations, a log transformation and a reverse log transformation, were attempted to normalize it.

Log and reverse log transformations of somatic anxiety data

at_no.outliers$ln.som.anx_lp = log(at_no.outliers$som.anx_lp)
at_no.outliers$ln.som.anx_mp = log(at_no.outliers$som.anx_mp)
at_no.outliers$ln.som.anx_hp = log(at_no.outliers$som.anx_hp)
at_no.outliers$rln.som.anx_lp = log((max(at_no.outliers$som.anx_lp+1)-at_no.outliers$som.anx_lp))
at_no.outliers$rln.som.anx_mp = log((max(at_no.outliers$som.anx_mp+1)-at_no.outliers$som.anx_mp))
at_no.outliers$rln.som.anx_hp = log((max(at_no.outliers$som.anx_hp+1)-at_no.outliers$som.anx_hp))

Q-Q plots of log and reverse log transformed somatic anxiety data

qqnorm(at_no.outliers$ln.som.anx_lp, datax = T, main = "Low-Pressure Post-Test Somatic Anxiety (log)")

qqnorm(at_no.outliers$ln.som.anx_mp, datax = T, main = "Mild-Pressure Post-Test Somatic Anxiety (log)")

qqnorm(at_no.outliers$ln.som.anx_hp, datax = T, main = "High-Pressure Post-Test Somatic Anxiety (log)")

qqnorm(at_no.outliers$rln.som.anx_lp, datax = T, main = "Low-Pressure Post-Test 
Reverse Somatic Anxiety (log)")

qqnorm(at_no.outliers$rln.som.anx_mp, datax = T, main = "Mild-Pressure Post-Test Reverse Somatic Anxiety (log)")

qqnorm(at_no.outliers$rln.som.anx_hp, datax = T, main = "High-Pressure Post-Test Reverse Somatic Anxiety (log)")

Shapiro-Wilk tests of log and reverse log transformed somatic anxiety data

shapiro.test(at_no.outliers$ln.som.anx_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.som.anx_lp
## W = 0.70929, p-value = 2.71e-11

shapiro.test(at_no.outliers$ln.som.anx_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.som.anx_mp
## W = 0.80689, p-value = 7.456e-09

shapiro.test(at_no.outliers$ln.som.anx_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.som.anx_hp
## W = 0.90825, p-value = 2.766e-05

shapiro.test(at_no.outliers$rln.som.anx_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.som.anx_lp
## W = 0.5694, p-value = 5.869e-14

shapiro.test(at_no.outliers$rln.som.anx_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.som.anx_mp
## W = 0.64624, p-value = 1.384e-12

shapiro.test(at_no.outliers$rln.som.anx_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.som.anx_hp
## W = 0.81325, p-value = 1.14e-08

Mental effort

Q-Q plots for mental effort

qqnorm(at_no.outliers$men.eff_lp, datax = T, main = "Low-Pressure Post-Test Mental Effort")

qqnorm(at_no.outliers$men.eff_mp, datax = T, main = "Mild-Pressure Post-Test Mental Effort")

qqnorm(at_no.outliers$men.eff_hp, datax = T, main = "High-Pressure Post-Test Mental Effort")

Shapiro-Wilk tests for mental effort

shapiro.test(at_no.outliers$men.eff_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$men.eff_lp
## W = 0.96632, p-value = 0.03318

shapiro.test(at_no.outliers$men.eff_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$men.eff_mp
## W = 0.97165, p-value = 0.07233

shapiro.test(at_no.outliers$men.eff_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$men.eff_hp
## W = 0.98317, p-value = 0.3759

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that mental effort data were normally distributed.

Movement reinvestment

Q-Q plots for movement reinvestment

qqnorm(at_no.outliers$rein_lp, datax = T, main = "Low-Pressure Post-Test Movement Reinvestment")

qqnorm(at_no.outliers$rein_mp, datax = T, main = "Mild-Pressure Post-Test Movement Reinvestment")

qqnorm(at_no.outliers$rein_hp, datax = T, main = "High-Pressure Post-Test Movement Reinvestment")

Shapiro-Wilk tests for movement reinvestment

shapiro.test(at_no.outliers$rein_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rein_lp
## W = 0.945, p-value = 0.001804

shapiro.test(at_no.outliers$rein_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rein_mp
## W = 0.93996, p-value = 0.0009584

shapiro.test(at_no.outliers$rein_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rein_hp
## W = 0.92389, p-value = 0.0001459

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that movement reinvestment data were non-normally distributed. Thus, two transformations, a log transformation and a reverse log transformation, were attempted to normalize it.

Log and reverse log transformations of movement reinvestment data

at_no.outliers$ln.rein_lp = log(at_no.outliers$rein_lp)
at_no.outliers$ln.rein_mp = log(at_no.outliers$rein_mp)
at_no.outliers$ln.rein_hp = log(at_no.outliers$rein_hp)
at_no.outliers$rln.rein_lp = log((max(at_no.outliers$rein_lp+1)-at_no.outliers$rein_lp))
at_no.outliers$rln.rein_mp = log((max(at_no.outliers$rein_mp+1)-at_no.outliers$rein_mp))
at_no.outliers$rln.rein_hp = log((max(at_no.outliers$rein_hp+1)-at_no.outliers$rein_hp))

Q-Q plots of log and reverse log transformed movement reinvestment data

qqnorm(at_no.outliers$ln.rein_lp, datax = T, main = "Low-Pressure Post-Test Movement Reinvestment (log)")

qqnorm(at_no.outliers$ln.rein_mp, datax = T, main = "Mild-Pressure Post-Test Movement Reinvestment (log)")

qqnorm(at_no.outliers$ln.rein_hp, datax = T, main = "High-Pressure Post-Test Movement Reinvestment (log)")

qqnorm(at_no.outliers$rln.rein_lp, datax = T, main = "Low-Pressure Post-Test Reverse Movement Reinvestment (log)")

qqnorm(at_no.outliers$rln.rein_mp, datax = T, main = "Mild-Pressure Post-Test Reverse Movement Reinvestment (log)")

qqnorm(at_no.outliers$rln.rein_hp, datax = T, main = "High-Pressure Post-Test Reverse Movement Reinvestment (log)")

Shapiro-Wilk tests of log and reverse log transformed movement reinvestment data

shapiro.test(at_no.outliers$ln.rein_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.rein_lp
## W = 0.87742, p-value = 1.529e-06

shapiro.test(at_no.outliers$ln.rein_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.rein_mp
## W = 0.92767, p-value = 0.0002233

shapiro.test(at_no.outliers$ln.rein_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.rein_hp
## W = 0.9077, p-value = 2.615e-05

shapiro.test(at_no.outliers$rln.rein_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.rein_lp
## W = 0.95362, p-value = 0.005583

shapiro.test(at_no.outliers$rln.rein_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.rein_mp
## W = 0.93537, p-value = 0.0005485

shapiro.test(at_no.outliers$rln.rein_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.rein_hp
## W = 0.92875, p-value = 0.0002525

Challenge-threat

Q-Q plots for challenge-threat

qqnorm(at_no.outliers$ct_lp, datax = T, main = "Low-Pressure Post-Test Challenge-Threat")

qqnorm(at_no.outliers$ct_mp, datax = T, main = "Mild-Pressure Post-Test Challenge-Threat")

qqnorm(at_no.outliers$ct_hp, datax = T, main = "High-Pressure Post-Test Challenge-Threat")

Shapiro-Wilk tests for challenge-threat

shapiro.test(at_no.outliers$ct_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ct_lp
## W = 0.79654, p-value = 3.802e-09

shapiro.test(at_no.outliers$ct_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ct_mp
## W = 0.75416, p-value = 2.977e-10

shapiro.test(at_no.outliers$ct_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ct_hp
## W = 0.74142, p-value = 1.466e-10

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that challenge-threat data were non-normally distributed. Thus, two transformations, a log transformation and a reverse log transformation, were attempted to normalize it.

Log and reverse log transformations of challenge-threat data

at_no.outliers$ln.ct_lp = log(at_no.outliers$ct_lp)
at_no.outliers$ln.ct_mp = log(at_no.outliers$ct_mp)
at_no.outliers$ln.ct_hp = log(at_no.outliers$ct_hp)
at_no.outliers$rln.ct_lp = log((max(at_no.outliers$ct_lp+1)-at_no.outliers$ct_lp))
at_no.outliers$rln.ct_mp = log((max(at_no.outliers$ct_mp+1)-at_no.outliers$ct_mp))
at_no.outliers$rln.ct_hp = log((max(at_no.outliers$ct_hp+1)-at_no.outliers$ct_hp))

Q-Q plots of log and reverse log transformed challenge-threat data

qqnorm(at_no.outliers$ln.ct_lp, datax = T, main = "Low-Pressure Post-Test Challenge-Threat (log)")

qqnorm(at_no.outliers$ln.ct_mp, datax = T, main = "Mild-Pressure Post-Test Challenge-Threat (log)")

qqnorm(at_no.outliers$ln.ct_hp, datax = T, main = "High-Pressure Post-Test Challenge-Threat (log)")

qqnorm(at_no.outliers$rln.ct_lp, datax = T, main = "Low-Pressure Post-Test Reverse Challenge-Threat (log)")

qqnorm(at_no.outliers$rln.ct_mp, datax = T, main = "Mild-Pressure Post-Test Reverse Challenge-Threat (log)")

qqnorm(at_no.outliers$rln.ct_hp, datax = T, main = "High-Pressure Post-Test Reverse Challenge-Threat (log)")

Shapiro-Wilk tests of log and reverse log transformed challenge-threat data

shapiro.test(at_no.outliers$ln.ct_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.ct_lp
## W = 0.89058, p-value = 4.985e-06

shapiro.test(at_no.outliers$ln.ct_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.ct_mp
## W = 0.91535, p-value = 5.774e-05

shapiro.test(at_no.outliers$ln.ct_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.ct_hp
## W = 0.93961, p-value = 0.0009176

shapiro.test(at_no.outliers$rln.ct_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.ct_lp
## W = 0.71765, p-value = 4.152e-11

shapiro.test(at_no.outliers$rln.ct_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.ct_mp
## W = 0.65423, p-value = 1.975e-12

shapiro.test(at_no.outliers$rln.ct_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.ct_hp
## W = 0.58624, p-value = 1.131e-13

Self-confidence

Q-Q plots for self-confidence

qqnorm(at_no.outliers$sc_lp, datax = T, main = "Low-Pressure Post-Test Self-Confidence")

qqnorm(at_no.outliers$sc_mp, datax = T, main = "Mild-Pressure Post-Test Self-Confidence")

qqnorm(at_no.outliers$sc_hp, datax = T, main = "High-Pressure Post-Test Self-Confidence")

Shapiro-Wilk tests for self-confidence

shapiro.test(at_no.outliers$sc_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$sc_lp
## W = 0.96145, p-value = 0.0165

shapiro.test(at_no.outliers$sc_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$sc_mp
## W = 0.95821, p-value = 0.01047

shapiro.test(at_no.outliers$sc_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$sc_hp
## W = 0.9569, p-value = 0.008741

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that self-confidence data were non-normally distributed. Thus, two transformations, a log transformation and a reverse log transformation, were attempted to normalize it.

Log and reverse log transformations of self-confidence data

at_no.outliers$ln.sc_lp = log(at_no.outliers$sc_lp)
at_no.outliers$ln.sc_mp = log(at_no.outliers$sc_mp)
at_no.outliers$ln.sc_hp = log(at_no.outliers$sc_hp)
at_no.outliers$rln.sc_lp = log((max(at_no.outliers$sc_lp+1)-at_no.outliers$sc_lp))
at_no.outliers$rln.sc_mp = log((max(at_no.outliers$sc_mp+1)-at_no.outliers$sc_mp))
at_no.outliers$rln.sc_hp = log((max(at_no.outliers$sc_hp+1)-at_no.outliers$sc_hp))

Q-Q plots of log and reverse log transformed challenge-threat data

qqnorm(at_no.outliers$ln.sc_lp, datax = T, main = "Low-Pressure Post-Test Self-Confidence (log)")

qqnorm(at_no.outliers$ln.sc_mp, datax = T, main = "Mild-Pressure Post-Test Self-Confidence (log)")

qqnorm(at_no.outliers$ln.sc_hp, datax = T, main = "High-Pressure Post-Test Self-Confidence (log)")

qqnorm(at_no.outliers$rln.sc_lp, datax = T, main = "Low-Pressure Post-Test Reverse Self-Confidence (log)")

qqnorm(at_no.outliers$rln.sc_mp, datax = T, main = "Mild-Pressure Post-Test Reverse Self-Confidence (log)")

qqnorm(at_no.outliers$rln.sc_hp, datax = T, main = "High-Pressure Post-Test Reverse Self-Confidence (log)")

Shapiro-Wilk tests of log and reverse log transformed challenge-threat data

shapiro.test(at_no.outliers$ln.sc_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.sc_lp
## W = 0.90728, p-value = 2.505e-05

shapiro.test(at_no.outliers$ln.sc_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.sc_mp
## W = 0.90036, p-value = 1.262e-05

shapiro.test(at_no.outliers$ln.sc_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$ln.sc_hp
## W = 0.89077, p-value = 5.073e-06

shapiro.test(at_no.outliers$rln.sc_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.sc_lp
## W = 0.93957, p-value = 0.0009128

shapiro.test(at_no.outliers$rln.sc_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.sc_mp
## W = 0.93195, p-value = 0.000366

shapiro.test(at_no.outliers$rln.sc_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$rln.sc_hp
## W = 0.96073, p-value = 0.0149

Heart rate

Q-Q plots for heart rate

qqnorm(at_no.outliers$hr_lp, datax = T, main = "Low-Pressure Post-Test Heart Rate")

qqnorm(at_no.outliers$hr_mp, datax = T, main = "Mild-Pressure Post-Test Heart Rate")

qqnorm(at_no.outliers$hr_hp, datax = T, main = "High-Pressure Post-Test Heart Rate")

Shapiro-Wilk tests for heart rate

shapiro.test(at_no.outliers$hr_lp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$hr_lp
## W = 0.96937, p-value = 0.05984

shapiro.test(at_no.outliers$hr_mp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$hr_mp
## W = 0.97236, p-value = 0.09154

shapiro.test(at_no.outliers$hr_hp)

## 
##  Shapiro-Wilk normality test
## 
## data:  at_no.outliers$hr_hp
## W = 0.97197, p-value = 0.08655

Taken together, Q-Q plots and Shapiro-Wilk tests indicated that heart rate data were normally distributed.

Demographic data table

st(at_no.outliers, vars = c('sex','age','golf.life','golf.yr'), group = 'group')

Summary Statistics
group	at			cg
Variable	N	Mean	SD	N	Mean	SD
sex	41			39
… F	17	41.5%		17	43.6%
… M	24	58.5%		22	56.4%
age	41	22.415	3.879	39	22.846	3.822
golf.life	41	1.488	0.637	39	1.462	0.682
golf.yr	41	0.585	0.547	39	0.462	0.643

Creating long dataframe for putting and heart data

at_no.outliers.putt.heart <-select(at_no.outliers, id, group, re_pre:hf_hp)

at_no.outliers.putt.heart.long <- at_no.outliers.putt.heart %>%
  pivot_longer(
    !id & !group & !re_pre & !bve_pre & !hr_pre & !rmssd_pre & !hf_pre, 
    names_to = c(".value","phase"),
               names_sep = "_")

Creating long dataframe for putting and heart data including outliers

at_putt.heart <-select(at, id, group, re_pre:hf_hp)

at_putt.heart.long <- at_putt.heart %>%
  pivot_longer(
    !id & !group & !re_pre & !bve_pre & !hr_pre & !rmssd_pre & !hf_pre, 
    names_to = c(".value","phase"),
               names_sep = "_")

Creating long dataframe for putting and heart data excluding participants who did not follow pre-experiment instructions for Day 3

at_fail.instruct.putt.heart <-select(at_fail.instruct, id, group, re_pre:hf_hp)

at_fail.instruct.putt.heart.long <- at_fail.instruct.putt.heart %>%
  pivot_longer(
    !id & !group & !re_pre & !bve_pre & !hr_pre & !rmssd_pre & !hf_pre, 
    names_to = c(".value","phase"),
               names_sep = "_")

Creating long dataframe for questionnaire data

at_no.outliers.quest <-select(at_no.outliers, id, group, men.eff_pre:men.eff_hp, cog.anx_pre:ct_hp)

at_no.outliers.quest.long <- at_no.outliers.quest %>%
  pivot_longer(
    !id & !group & !men.eff_pre & !sc_pre & !ct_pre & !rein_pre, 
    names_to = c(".value","phase"),
               names_sep = "_")

Group manipulation check

Cognitive anxiety

We deviated from our planned ANCOVA based on the recommendation of an anonymous reviewer.

cog.anx.group.check.model <- aov_ez("id","cog.anx", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "pre" | phase =="d01"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(cog.anx.group.check.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value  Pr(>F)    
## (Intercept) 550.59      1   52.135     78 823.7517 < 2e-16 ***
## group         0.10      1   52.135     78   0.1478 0.70165    
## phase         0.02      1    8.887     78   0.1992 0.65661    
## group:phase   0.86      1    8.887     78   7.5717 0.00737 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(cog.anx.group.check.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.67	0.15	.002	.702
phase	1, 78	0.11	0.20	.003	.657
group:phase	1, 78	0.11	7.57 **	.088	.007

There was a significant Group x Phase interaction, so paired t-tests (phase) were conducted for each group.

t.test(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "pre" | phase == "d01"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  cog.anx by phase
## t = 1.8884, df = 40, p-value = 0.06623
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.01199079  0.35345421
## sample estimates:
## mean of the differences 
##               0.1707317

t.test(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "pre" | phase == "d01"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  cog.anx by phase
## t = -2.2667, df = 38, p-value = 0.02918
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.23299610 -0.01315775
## sample estimates:
## mean of the differences 
##              -0.1230769

Effect sizes were calculated for the paired-t-tests.

cohen.d(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "pre" |    phase == "d01"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.2862169 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.02151644  0.59395021

cohen.d(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "pre" |    phase == "d01"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.1804538 (negligible)
## 95 percent confidence interval:
##       lower       upper 
## -0.34029644 -0.02061109

Somatic anxiety

We deviated from our planned ANCOVA based on the recommendation of an anonymous reviewer.

som.anx.group.check.model <- aov_ez("id","som.anx", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "pre" | phase =="d01"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(som.anx.group.check.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 301.207      1  16.4561     78 1427.6862 < 2.2e-16 ***
## group         2.967      1  16.4561     78   14.0644 0.0003376 ***
## phase         0.112      1   4.4025     78    1.9779 0.1635864    
## group:phase   0.403      1   4.4025     78    7.1484 0.0091354 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(som.anx.group.check.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.21	14.06 ***	.153	<.001
phase	1, 78	0.06	1.98	.025	.164
group:phase	1, 78	0.06	7.15 **	.084	.009

There was a significant Group x Phase interaction, so paired t-tests (phase) were conducted for each group.

t.test(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "pre" | phase == "d01"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  som.anx by phase
## t = 2.4341, df = 40, p-value = 0.01949
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.02601596 0.28060425
## sample estimates:
## mean of the differences 
##               0.1533101

t.test(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "pre" | phase == "d01"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  som.anx by phase
## t = -1.2089, df = 38, p-value = 0.2342
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.12735802  0.03211993
## sample estimates:
## mean of the differences 
##             -0.04761905

Effect sizes were calculated for the paired-t-tests.

cohen.d(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "pre" |    phase == "d01"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.3628102 (small)
## 95 percent confidence interval:
##      lower      upper 
## 0.05658385 0.66903662

cohen.d(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "pre" |    phase == "d01"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.1508979 (negligible)
## 95 percent confidence interval:
##       lower       upper 
## -0.40090600  0.09911029

Creating long format dataset for HR manipulation check, accuracy figure, and HR table

at_no.outliers.putt.heart.fig <-select(at_no.outliers, id, group, re_pre:re_hp, hr_pre:hr_hp)

at_no.outliers.putt.heart.fig.long <- at_no.outliers.putt.heart.fig %>%
  pivot_longer(
    !id & !group, 
    names_to = c(".value","phase"),
               names_sep = "_")

Heart rate

We deviated from our planned ANCOVA based on the recommendation of an anonymous reviewer.

hr.group.check.model <- aov_ez("id","hr", at_no.outliers.putt.heart.fig.long %>% filter(at_no.outliers.putt.heart.fig.long$phase == "pre" | phase =="d01.e"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(hr.group.check.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value Pr(>F)    
## (Intercept) 1239455      1  29916.9     77 3190.1088 <2e-16 ***
## group             1      1  29916.9     77    0.0016 0.9681    
## phase            15      1   1034.3     77    1.0966 0.2983    
## group:phase       0      1   1034.3     77    0.0155 0.9013    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(hr.group.check.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 77	388.53	0.00	<.001	.968
phase	1, 77	13.43	1.10	.014	.298
group:phase	1, 77	13.43	0.02	<.001	.901

Post-test manipulation check

Cognitive anxiety

cog.anx_post.man.check <- aov_ez("id","cog.anx", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "lp" | phase == "mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(cog.anx_post.man.check)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 911.38      1   77.293     78 919.7148 < 2.2e-16 ***
## group         0.36      1   77.293     78   0.3631    0.5485    
## phase        15.62      2   29.806    156  40.8817 5.302e-15 ***
## group:phase   0.48      2   29.806    156   1.2577    0.2872    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic p-value
## phase              0.94843 0.13023
## group:phase        0.94843 0.13023
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.95096  2.196e-14 ***
## group:phase 0.95096     0.2863    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.9740814 1.123556e-14
## group:phase 0.9740814 2.867538e-01

knitr::kable(nice(cog.anx_post.man.check), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.99	0.36	.005	.549
phase	1.90, 148.35	0.20	40.88 ***	.344	<.001
group:phase	1.90, 148.35	0.20	1.26	.016	.286

Since there was a main effect of phase for cognitive anxiety, paired t-tests were conducted between each post-test, and a Bonferroni correction should be applied to the p-values below. The t-tests and Bonferroni correction deviate from our analysis plan and were done at the recommendation of an anonymous reviewer. We planned to conduct one-tailed Wilcoxon signed-rank tests with no Bonferroni correction.

t.test(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  cog.anx by phase
## t = -4.3275, df = 79, p-value = 4.374e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.3978369 -0.1471631
## sample estimates:
## mean of the differences 
##                 -0.2725

t.test(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  cog.anx by phase
## t = 8.248, df = 79, p-value = 2.863e-12
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.4722754 0.7727246
## sample estimates:
## mean of the differences 
##                  0.6225

t.test(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  cog.anx by phase
## t = 5.097, df = 79, p-value = 2.304e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.2133213 0.4866787
## sample estimates:
## mean of the differences 
##                    0.35

Effect sizes were calculated for the paired-t-tests.

cohen.d(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.4172006 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.6157249 -0.2186762

cohen.d(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.9123197 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.6523388 1.1723005

cohen.d(cog.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.4831222 (small)
## 95 percent confidence interval:
##     lower     upper 
## 0.2852910 0.6809535

Somatic anxiety

som.anx_post.man.check <- aov_ez("id","som.anx", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "lp" | phase == "mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(som.anx_post.man.check)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 421.37      1   28.412     78 1156.7904 < 2.2e-16 ***
## group         0.07      1   28.412     78    0.2054    0.6517    
## phase         5.63      2   11.392    156   38.5757 2.443e-14 ***
## group:phase   0.23      2   11.392    156    1.5706    0.2112    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic    p-value
## phase              0.76815 3.8883e-05
## group:phase        0.76815 3.8883e-05
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.81179  4.335e-12 ***
## group:phase 0.81179     0.2148    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.8265824 2.884443e-12
## group:phase 0.8265824 2.145794e-01

knitr::kable(nice(som.anx_post.man.check), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.36	0.21	.003	.652
phase	1.62, 126.64	0.09	38.58 ***	.331	<.001
group:phase	1.62, 126.64	0.09	1.57	.020	.215

Since there was a main effect of phase for somatic anxiety, paired t-tests were conducted between each post-test, and a Bonferroni correction should be applied to the p-values below. The t-tests and Bonferroni correction deviate from our analysis plan and were done at the recommendation of an anonymous reviewer. We planned to conduct one-tailed Wilcoxon signed-rank tests with no Bonferroni correction.

t.test(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  som.anx by phase
## t = -3.714, df = 79, p-value = 0.0003787
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.20570450 -0.06215264
## sample estimates:
## mean of the differences 
##              -0.1339286

t.test(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  som.anx by phase
## t = 7.1255, df = 79, p-value = 4.296e-10
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.2663862 0.4728996
## sample estimates:
## mean of the differences 
##               0.3696429

t.test(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  som.anx by phase
## t = 6.0364, df = 79, p-value = 4.838e-08
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.1579898 0.3134387
## sample estimates:
## mean of the differences 
##               0.2357143

Effect sizes were calculated for the paired-t-tests.

cohen.d(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.3623064 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.5612003 -0.1634125

cohen.d(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.8186863 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.5564757 1.0808969

cohen.d(som.anx ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.4776612 (small)
## 95 percent confidence interval:
##     lower     upper 
## 0.3126984 0.6426240

Heart rate

hr_post.man.check <- aov_ez("id","hr", at_no.outliers.putt.heart.long %>% filter(at_no.outliers.putt.heart.long$phase == "lp" | phase == "mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(hr_post.man.check)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 1819490      1    42297     75 3226.2828 < 2.2e-16 ***
## group           404      1    42297     75    0.7157    0.4002    
## phase           491      2     2243    150   16.4043 3.607e-07 ***
## group:phase      19      2     2243    150    0.6379    0.5299    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic p-value
## phase              0.97884 0.45326
## group:phase        0.97884 0.45326
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.97928  4.586e-07 ***
## group:phase 0.97928     0.5267    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##               HF eps   Pr(>F[HF])
## phase       1.005254 3.606616e-07
## group:phase 1.005254 5.298513e-01

knitr::kable(nice(hr_post.man.check), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 75	563.96	0.72	.009	.400
phase	1.96, 146.89	15.27	16.40 ***	.179	<.001
group:phase	1.96, 146.89	15.27	0.64	.008	.527

Since there was a main effect of phase for heart rate, paired t-tests were conducted between each post-test and a Bonferroni correction should be applied to the p-values below. The two-tailed (as opposed to one-tailed) t-tests and Bonferroni correction deviate from our analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(hr ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  hr by phase
## t = -1.4633, df = 76, p-value = 0.1475
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.156047  0.329722
## sample estimates:
## mean of the differences 
##              -0.9131623

t.test(hr ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  hr by phase
## t = 5.2152, df = 76, p-value = 1.537e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  2.124665 4.750111
## sample estimates:
## mean of the differences 
##                3.437388

t.test(hr ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  hr by phase
## t = 4.3554, df = 76, p-value = 4.098e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.369933 3.678519
## sample estimates:
## mean of the differences 
##                2.524226

Effect sizes were calculated for the pairedt-tests.

cohen.d(hr ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.06269618 (negligible)
## 95 percent confidence interval:
##       lower       upper 
## -0.21339016  0.08799779

cohen.d(hr ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.219076 (small)
## 95 percent confidence interval:
##      lower      upper 
## 0.08212986 0.35602217

cohen.d(hr ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.1583339 (negligible)
## 95 percent confidence interval:
##      lower      upper 
## 0.04984962 0.26681821

Self-confidence

Post-test

sc_posttest.model <- aov_ez("id","sc", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "lp" | phase == "mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(sc_posttest.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value Pr(>F)    
## (Intercept) 1805.23      1  139.545     78 1009.0514 <2e-16 ***
## group          2.62      1  139.545     78    1.4618 0.2303    
## phase          0.24      2   18.548    156    1.0165 0.3643    
## group:phase    0.50      2   18.548    156    2.0930 0.1268    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic p-value
## phase              0.99446 0.80731
## group:phase        0.99446 0.80731
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])
## phase       0.99449     0.3639
## group:phase 0.99449     0.1271
## 
##               HF eps Pr(>F[HF])
## phase       1.020436  0.3642590
## group:phase 1.020436  0.1267641

knitr::kable(nice(sc_posttest.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	1.79	1.46	.018	.230
phase	1.99, 155.14	0.12	1.02	.013	.364
group:phase	1.99, 155.14	0.12	2.09	.026	.127

Practice

sc_practice.model.no.outliers <- aov_ez("id","sc", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "d01" | phase == "d02"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(sc_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value Pr(>F)    
## (Intercept) 1258.80      1   72.038     78 1362.9746 <2e-16 ***
## group          1.06      1   72.038     78    1.1470 0.2875    
## phase          0.00      1    9.985     78    0.0229 0.8800    
## group:phase    0.07      1    9.985     78    0.5698 0.4526    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(sc_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.92	1.15	.014	.287
phase	1, 78	0.13	0.02	<.001	.880
group:phase	1, 78	0.13	0.57	.007	.453

Primary analysis–Putting accuracy during post-tests

re_post.model.no.outliers <- aov_ez("id","re", at_no.outliers.putt.heart.long %>% filter(at_no.outliers.putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df   F value  Pr(>F)    
## (Intercept) 495513      1    28622     78 1350.3481 < 2e-16 ***
## group          428      1    28622     78    1.1652 0.28371    
## phase          467      2    20892    156    1.7440 0.17821    
## group:phase   2564      2    20892    156    9.5715 0.00012 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic    p-value
## phase              0.83307 0.00088375
## group:phase        0.83307 0.00088375
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.85695  0.1833016    
## group:phase 0.85695  0.0002921 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.8743306 0.1827155275
## group:phase 0.8743306 0.0002621456

knitr::kable(nice(re_post.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	366.95	1.17	.015	.284
phase	1.71, 133.68	156.28	1.74	.022	.183
group:phase	1.71, 133.68	156.28	9.57 ***	.109	<.001

The Group x Post-test interaction was significant, so separate ANOVAs (post-test) were conducted for each group.

AT group

re_post.model.no.outliers.at <- aov_ez("id", "re", at_no.outliers.putt.heart.long %>% filter(at_no.outliers.putt.heart.long$group == "at", at_no.outliers.putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.no.outliers.at)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df F value Pr(>F)    
## (Intercept) 239400      1    12823     40 746.771 <2e-16 ***
## phase          436      2    12417     80   1.403 0.2518    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic  p-value
## phase        0.83067 0.026846
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])
## phase 0.85519      0.252
## 
##          HF eps Pr(>F[HF])
## phase 0.8896116  0.2520897

knitr::kable(nice(re_post.model.no.outliers.at), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.71, 68.42	181.49	1.40	.034	.252

Control group

re_post.model.no.outliers.cg <- aov_ez("id", "re", at_no.outliers.putt.heart.long %>% filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.no.outliers.cg)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df F value    Pr(>F)    
## (Intercept) 256123      1  15799.1     38  616.03 < 2.2e-16 ***
## phase         2543      2   8475.1     76   11.40 4.678e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic  p-value
## phase        0.83653 0.036807
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##       GG eps Pr(>F[GG])    
## phase 0.8595  0.0001276 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps   Pr(>F[HF])
## phase 0.8963505 9.805553e-05

knitr::kable(nice(re_post.model.no.outliers.cg), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.72, 65.32	129.74	11.40 ***	.231	<.001

There was a significant effect of post-test for the control group, so paired t-tests were conducted between each pair of post-tests. A Bonferonni correction should be applied to the p-values below. The two-tailed (as opposed to one-tailed) t-tests and Bonferroni corrections (as opposed to no corrections) deviate from our analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(re ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = -3.135, df = 38, p-value = 0.003309
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -9.565998 -2.059131
## sample estimates:
## mean of the differences 
##               -5.812564

t.test(re ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = 4.4678, df = 38, p-value = 6.891e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   6.244472 16.591938
## sample estimates:
## mean of the differences 
##                11.41821

t.test(re ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = 2.091, df = 38, p-value = 0.04326
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   0.1786328 11.0326493
## sample estimates:
## mean of the differences 
##                5.605641

Effect sizes were calculated for the paired-t-tests.

cohen.d(re ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.3770054 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.6248843 -0.1291264

cohen.d(re ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.7958023 (medium)
## 95 percent confidence interval:
##     lower     upper 
## 0.3887319 1.2028727

cohen.d(re ~ phase, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$group == "cg", at_no.outliers.putt.heart.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.3361817 (small)
## 95 percent confidence interval:
##       lower       upper 
## 0.007050725 0.665312628

Because of the significant Group x Post-test interaction, t-tests were conducted between groups for each post-test. We deviated from our analysis plan at the recommendation of an anonymous reviewer to make all t-tests two-tailed. Additionally, a Bonferroni correction should be applied to p-values below, which is a deviation from our analysis plan and done at the recommendation of an anonymous reviewer.

t.test(re ~ group, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$phase == "lp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = 1.9018, df = 72.453, p-value = 0.06117
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -0.2534498 10.8008545
## sample estimates:
## mean in group at mean in group cg 
##          46.3178          41.0441

t.test(re ~ group, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$phase == "mp"), alternative = "less", paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = -0.74771, df = 75.064, p-value = 0.2285
## alternative hypothesis: true difference in means between group at and group cg is less than 0
## 95 percent confidence interval:
##      -Inf 3.121726
## sample estimates:
## mean in group at mean in group cg 
##         44.31317         46.85667

t.test(re ~ group, at_no.outliers.putt.heart.long %>% 
         filter(at_no.outliers.putt.heart.long$phase == "hp"), alternative = "less", paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = -3.037, df = 76.676, p-value = 0.001632
## alternative hypothesis: true difference in means between group at and group cg is less than 0
## 95 percent confidence interval:
##       -Inf -4.852671
## sample estimates:
## mean in group at mean in group cg 
##         41.72098         52.46231

Effect sizes were calculated for the t-tests.

cohen.d(re_lp ~ group, at_no.outliers, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.4178456 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.02794838  0.86363962

cohen.d(re_mp ~ group, at_no.outliers, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.1662531 (negligible)
## 95 percent confidence interval:
##      lower      upper 
## -0.6080244  0.2755181

cohen.d(re_hp ~ group, at_no.outliers, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.6741381 (medium)
## 95 percent confidence interval:
##      lower      upper 
## -1.1274944 -0.2207817

Putting accuracy figure

Creating figure

re_plot.no.outliers<-aov_ez("id", "re", at_no.outliers.putt.heart.fig.long, between = "group", within = "phase")

afex_plot(re_plot.no.outliers, x = "phase", panel = "group", error = "within",
          point_arg = list(size = 2),
          error_arg = list(size = 1, width = 0),
          factor_levels = list(phase = c("Pre-Test", "Prac 1 Early", "Prac 1 Mid", "Prac 1 Late", "Prac 2 Early", "Prac 2 Mid", "Prac 2 Late", "LP Post-Test", "MP Post-Test", "HP Post-Test"), group = (c("Anxiety Training", "Control")))) +
  labs(y = "Radial Error (cm)", x = "Phase") +
  theme_bw(base_size = 15) +
  geom_line(aes(group = 10), size = 1) +
  theme(axis.text.x = element_text(angle = 90))

ggsave(here("output", "re_phase.group.no.outliers.png"))

Mechanistic variables during post-tests

Mental effort

men_eff.post.model <- aov_ez("id","men.eff", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(men_eff.post.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 1589116      1   177622     78 697.8363 < 2.2e-16 ***
## group           303      1   177622     78   0.1329  0.716402    
## phase         13208      2    13318    156  77.3547 < 2.2e-16 ***
## group:phase    1003      2    13318    156   5.8749  0.003468 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic    p-value
## phase              0.74002 9.2428e-06
## group:phase        0.74002 9.2428e-06
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.79366  < 2.2e-16 ***
## group:phase 0.79366   0.006778 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.8074479 6.328872e-20
## group:phase 0.8074479 6.480384e-03

knitr::kable(nice(men_eff.post.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	2277.20	0.13	.002	.716
phase	1.59, 123.81	107.57	77.35 ***	.498	<.001
group:phase	1.59, 123.81	107.57	5.87 **	.070	.007

The Group x Post-test interaction was significant, so separate ANOVAs (post-test) were conducted for each group.

AT group

men_eff.post.at.model <- aov_ez("id", "men.eff", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(men_eff.post.at.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df F value    Pr(>F)    
## (Intercept) 837581      1    69610     40 481.299 < 2.2e-16 ***
## phase         3800      2     5071     80  29.974 1.927e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic  p-value
## phase        0.81152 0.017033
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])    
## phase 0.84141   3.88e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps   Pr(>F[HF])
## phase 0.8742225 2.083083e-09

knitr::kable(nice(men_eff.post.at.model), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.68, 67.31	75.33	29.97 ***	.428	<.001

There was a significant effect of post-test for the AT group, so paired t-tests were conducted between each pair of post-tests. A Bonferonni correction should be applied to the p-values below. The two-tailed (as opposed to one-tailed) t-tests and Bonferroni corrections (as opposed to no corrections) deviate from our analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  men.eff by phase
## t = -2.7369, df = 40, p-value = 0.009207
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -7.716999 -1.161050
## sample estimates:
## mean of the differences 
##               -4.439024

t.test(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  men.eff by phase
## t = 6.3616, df = 40, p-value = 1.467e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   9.119509 17.612198
## sample estimates:
## mean of the differences 
##                13.36585

t.test(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  men.eff by phase
## t = 5.9766, df = 40, p-value = 5.099e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   5.908068 11.945591
## sample estimates:
## mean of the differences 
##                8.926829

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.1775524 (negligible)
## 95 percent confidence interval:
##       lower       upper 
## -0.30766664 -0.04743808

cohen.d(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.5205402 (medium)
## 95 percent confidence interval:
##     lower     upper 
## 0.3470212 0.6940593

cohen.d(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.3446093 (small)
## 95 percent confidence interval:
##     lower     upper 
## 0.2265043 0.4627144

Control group

men_eff.post.cg.model <- aov_ez("id", "men.eff", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(men_eff.post.cg.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df F value    Pr(>F)    
## (Intercept) 753929      1   108012     38 265.242 < 2.2e-16 ***
## phase        10250      2     8247     76  47.227 4.676e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic    p-value
## phase        0.68344 0.00087492
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])    
## phase 0.75956  3.145e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps   Pr(>F[HF])
## phase 0.7845937 1.594571e-11

knitr::kable(nice(men_eff.post.cg.model), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.52, 57.73	142.87	47.23 ***	.554	<.001

There was a significant effect of post-test for the control group, so paired t-tests were conducted between each pair of post-tests. A Bonferonni correction should be applied to the p-values below. The two-tailed (as opposed to one-tailed) t-tests and Bonferroni corrections (as opposed to no corretions) deviate from our analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  men.eff by phase
## t = -5.1413, df = 38, p-value = 8.531e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -16.474827  -7.166199
## sample estimates:
## mean of the differences 
##               -11.82051

t.test(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  men.eff by phase
## t = 7.9067, df = 38, p-value = 1.511e-09
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  17.05395 28.79221
## sample estimates:
## mean of the differences 
##                22.92308

t.test(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  men.eff by phase
## t = 6.406, df = 38, p-value = 1.581e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   7.594007 14.611121
## sample estimates:
## mean of the differences 
##                11.10256

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.3456913 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.4835494 -0.2078331

cohen.d(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.679911 (medium)
## 95 percent confidence interval:
##     lower     upper 
## 0.4898779 0.8699442

cohen.d(men.eff ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.3530155 (small)
## 95 percent confidence interval:
##     lower     upper 
## 0.2398934 0.4661376

t.test(men.eff ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  men.eff by group
## t = 1.1821, df = 68.162, p-value = 0.2413
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -5.429978 21.216094
## sample estimates:
## mean in group at mean in group cg 
##         76.58537         68.69231

t.test(men.eff ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  men.eff by group
## t = 0.080987, df = 72.388, p-value = 0.9357
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -12.07941  13.10255
## sample estimates:
## mean in group at mean in group cg 
##         81.02439         80.51282

t.test(men.eff ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "hp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  men.eff by group
## t = -0.26478, df = 74.887, p-value = 0.7919
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -14.18502  10.85669
## sample estimates:
## mean in group at mean in group cg 
##         89.95122         91.61538

Movement reinvestment

rein.post.model <- aov_ez("id","rein", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(rein.post.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 3683.6      1  130.758     78 2197.3352 < 2.2e-16 ***
## group          1.4      1  130.758     78    0.8489   0.35971    
## phase          5.2      2   25.762    156   15.7414 5.926e-07 ***
## group:phase    1.5      2   25.762    156    4.6356   0.01107 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic  p-value
## phase              0.84351 0.001427
## group:phase        0.84351 0.001427
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.86468  2.676e-06 ***
## group:phase 0.86468    0.01505 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.8825148 2.193186e-06
## group:phase 0.8825148 1.445467e-02

knitr::kable(nice(rein.post.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	1.68	0.85	.011	.360
phase	1.73, 134.89	0.19	15.74 ***	.168	<.001
group:phase	1.73, 134.89	0.19	4.64 *	.056	.015

The Group x Post-test interaction was significant, so separate ANOVAs (post-test) were conducted for each group.

AT group

rein.post.at.model <- aov_ez("id", "rein", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(rein.post.at.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 1964.00      1   65.452     40 1200.2762 < 2.2e-16 ***
## phase          0.86      2    5.433     80    6.3546  0.002746 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic  p-value
## phase         0.8742 0.072686
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])   
## phase 0.88826    0.00405 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps  Pr(>F[HF])
## phase 0.9266209 0.003543546

knitr::kable(nice(rein.post.at.model), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.78, 71.06	0.08	6.35 **	.137	.004

Since there was a main effect of phase for movement reinvestment, paired t-tests were conducted between each post-test, and a Bonferroni correction should be applied to the p-values below. The t-tests and Bonferroni correction deviate from our analysis plan and were done at the recommendation of an anonymous reviewer. We planned to conduct one-tailed Wilcoxon signed-rank tests with no Bonferroni correction.

t.test(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  rein by phase
## t = -0.43929, df = 40, p-value = 0.6628
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.11383694  0.07318653
## sample estimates:
## mean of the differences 
##              -0.0203252

t.test(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  rein by phase
## t = 2.9677, df = 40, p-value = 0.005046
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.05964769 0.31433605
## sample estimates:
## mean of the differences 
##               0.1869919

t.test(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  rein by phase
## t = 2.6938, df = 40, p-value = 0.01027
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.04162246 0.29171087
## sample estimates:
## mean of the differences 
##               0.1666667

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.0255193 (negligible)
## 95 percent confidence interval:
##      lower      upper 
## -0.1411452  0.0901066

cohen.d(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.2339251 (small)
## 95 percent confidence interval:
##      lower      upper 
## 0.07493171 0.39291843

cohen.d(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "at", at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.2161615 (small)
## 95 percent confidence interval:
##      lower      upper 
## 0.05461692 0.37770611

Control group

rein.post.cg.model <- aov_ez("id", "rein", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(rein.post.cg.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 1726.93      1   65.306     38 1004.852 < 2.2e-16 ***
## phase          5.75      2   20.329     76   10.739 7.808e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic   p-value
## phase        0.77835 0.0096996
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])    
## phase 0.81857  0.0002623 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps   Pr(>F[HF])
## phase 0.8504303 0.0002118929

knitr::kable(nice(rein.post.cg.model), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.64, 62.21	0.33	10.74 ***	.220	<.001

t.test(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  rein by phase
## t = -3.1141, df = 38, p-value = 0.0035
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.5782313 -0.1226234
## sample estimates:
## mean of the differences 
##              -0.3504274

t.test(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  rein by phase
## t = 3.7999, df = 38, p-value = 0.0005088
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.2496017 0.8187743
## sample estimates:
## mean of the differences 
##                0.534188

t.test(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  rein by phase
## t = 1.9671, df = 38, p-value = 0.0565
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.005352335  0.372873702
## sample estimates:
## mean of the differences 
##               0.1837607

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.3559339 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.5906768 -0.1211910

cohen.d(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.5685731 (medium)
## 95 percent confidence interval:
##     lower     upper 
## 0.2473814 0.8897648

cohen.d(rein ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$group == "cg", at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.2306555 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.00596717  0.46727808

Because of the significant Group x Post-test interaction, independent t-tests were conducted to examine between-group differences for each post-test. A Bonferroni correction should be applied to the p-values below. The t-tests and Bonferroni correction deviate from our analysis plan and were done at the recommendation of an anonymous reviewer. We planned to conduct a two-tailed Wilcoxon ranked-sum test for the low-pressure post-test, and one-tailed Wilcoxon ranked-sum tests for the mild- and high-pressure post-test. We did not plan to use a Bonferonni correction for any of the tests.

t.test(rein ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  rein by group
## t = 1.8373, df = 71.45, p-value = 0.07033
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -0.0323424  0.7919838
## sample estimates:
## mean in group at mean in group cg 
##         3.926829         3.547009

t.test(rein ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  rein by group
## t = 0.28372, df = 76.109, p-value = 0.7774
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -0.2992845  0.3987217
## sample estimates:
## mean in group at mean in group cg 
##         3.947154         3.897436

t.test(rein ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "hp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  rein by group
## t = 0.19651, df = 77.96, p-value = 0.8447
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -0.2978909  0.3631400
## sample estimates:
## mean in group at mean in group cg 
##         4.113821         4.081197

Challenge-threat

ct.post.model <- aov_ez("id","ct", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "lp" | phase =="mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(ct.post.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 1385.70      1   766.24     78 141.0586 < 2.2e-16 ***
## group          3.12      1   766.24     78   0.3176    0.5747    
## phase         48.93      2   134.92    156  28.2883 3.292e-11 ***
## group:phase    0.63      2   134.92    156   0.3654    0.6945    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic    p-value
## phase               0.8205 0.00049213
## group:phase         0.8205 0.00049213
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.84782  7.466e-10 ***
## group:phase 0.84782     0.6595    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.8646646 5.282590e-10
## group:phase 0.8646646 6.637212e-01

knitr::kable(nice(ct.post.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	9.82	0.32	.004	.575
phase	1.70, 132.26	1.02	28.29 ***	.266	<.001
group:phase	1.70, 132.26	1.02	0.37	.005	.660

Because there was a main effect of post-test, paired t-tests were conducted between each post-test. A Bonferroni correction should be applied to the p-values below. The t-tests and Bonferroni correction deviate from our analysis plan and were done at the recommendation of an anonymous reviewer. We planned to conduct one-tailed Wilcoxon signed-rank tests with no Bonferroni correction.

t.test(ct ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  ct by phase
## t = 3.3635, df = 79, p-value = 0.001189
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.1898244 0.7401756
## sample estimates:
## mean of the differences 
##                   0.465

t.test(ct ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  ct by phase
## t = -6.3162, df = 79, p-value = 1.466e-08
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.4452773 -0.7526393
## sample estimates:
## mean of the differences 
##               -1.098958

t.test(ct ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  ct by phase
## t = -5.1832, df = 79, p-value = 1.635e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.8774106 -0.3905060
## sample estimates:
## mean of the differences 
##              -0.6339583

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(ct ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.2228019 (small)
## 95 percent confidence interval:
##      lower      upper 
## 0.09035688 0.35524702

cohen.d(ct ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.5615408 (medium)
## 95 percent confidence interval:
##      lower      upper 
## -0.7504720 -0.3726096

cohen.d(ct ~ phase, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.3175398 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.4415531 -0.1935266

Mechanistic variable figures

Creating long format dataset for figures and tables

at_no.outliers.quest.fig <-select(at_no.outliers, id, group, men.eff_pre:men.eff_hp, cog.anx_pre:ct_hp)

at_no.outliers.quest.fig.long <- at_no.outliers.quest.fig %>%
  pivot_longer(
    !id & !group, 
    names_to = c(".value","phase"),
               names_sep = "_")

Creating mental effort figure

men.eff_plot.no.outliers<-aov_ez("id", "men.eff", at_no.outliers.quest.fig.long, between = "group", within = "phase")

afex_plot(men.eff_plot.no.outliers, x = "phase", panel = "group", error = "within",
          point_arg = list(size = 2),
          error_arg = list(size = 1, width = 0),
          factor_levels = list(phase = c("Pre-Test", "Prac 1", "Prac 2", "LP Post-Test", "MP Post-Test", "HP Post-Test"), group = (c("Anxiety Training", "Control")))) +
  labs(y = "Mental Effort", x = "Phase") +
  theme_bw(base_size = 15) +
  geom_line(aes(group = 10), size = 1) +
  theme(axis.text.x = element_text(angle = 90))

ggsave(here("output", "men.eff_phase.group.no.outliers.png"))

Creating movement reinvestment figure

rein_plot.no.outliers<-aov_ez("id", "rein", at_no.outliers.quest.fig.long, between = "group", within = "phase")

afex_plot(rein_plot.no.outliers, x = "phase", panel = "group", error = "within",
          point_arg = list(size = 2),
          error_arg = list(size = 1, width = 0),
          factor_levels = list(phase = c("Pre-Test", "Prac 1", "Prac 2", "LP Post-Test", "MP Post-Test", "HP Post-Test"), group = (c("Anxiety Training", "Control")))) +
  labs(y = "Movement Reinvestment", x = "Phase") +
  theme_bw(base_size = 15) +
  geom_line(aes(group = 10), size = 1) +
  theme(axis.text.x = element_text(angle = 90))

ggsave(here("output", "rein_phase.group.no.outliers.png"))

Creating challenge-threat figure

ct_plot.no.outliers<-aov_ez("id", "ct", at_no.outliers.quest.fig.long, between = "group", within = "phase")

afex_plot(ct_plot.no.outliers, x = "phase", panel = "group", error = "within",
          point_arg = list(size = 2),
          error_arg = list(size = 1, width = 0),
          factor_levels = list(phase = c("Pre-Test", "Prac 1", "Prac 2", "LP Post-Test", "MP Post-Test", "HP Post-Test"), group = (c("Anxiety Training", "Control")))) +
  labs(y = "Challenge-Threat", x = "Phase") +
  theme_bw(base_size = 15) +
  geom_line(aes(group = 10), size = 1) +
  theme(axis.text.x = element_text(angle = 90))

ggsave(here("output", "ct_phase.group.no.outliers.png"))

Mediation of choking by mechanistic variables

Dummy coding group (AT = 1, control group = 0)

at_no.outliers$group_dummy <- with(at_no.outliers, ifelse(group=="at","1","0"))

The difference in radial error between each post-test was calculated, and then these difference scores were compared to determine which one had the largest effect size as a function of group and, thus, would serve as the dependent variable in the mediation analyses.

Calculate difference scores

at_no.outliers$re_diff.lp.mp = (at_no.outliers$re_mp - at_no.outliers$re_lp)
at_no.outliers$re_diff.lp.hp = (at_no.outliers$re_hp - at_no.outliers$re_lp)
at_no.outliers$re_diff.mp.hp = (at_no.outliers$re_hp - at_no.outliers$re_mp)

The low- minus high-pressure post-test difference score had the largest effect size as a function of group and would serve as the dependent variable.

t_test(at_no.outliers, re_diff.lp.mp ~ group)

## # A tibble: 1 x 8
##   .y.           group1 group2    n1    n2 statistic    df       p
## * <chr>         <chr>  <chr>  <int> <int>     <dbl> <dbl>   <dbl>
## 1 re_diff.lp.mp at     cg        41    39     -2.77  77.1 0.00695

cohen.d(re_diff.lp.mp ~ group, at_no.outliers, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.6118851 (medium)
## 95 percent confidence interval:
##      lower      upper 
## -1.0630911 -0.1606791

t_test(at_no.outliers, re_diff.lp.hp ~ group)

## # A tibble: 1 x 8
##   .y.           group1 group2    n1    n2 statistic    df         p
## * <chr>         <chr>  <chr>  <int> <int>     <dbl> <dbl>     <dbl>
## 1 re_diff.lp.hp at     cg        41    39     -4.11  77.0 0.0000962

cohen.d(re_diff.lp.hp ~ group, at_no.outliers, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.907809 (large)
## 95 percent confidence interval:
##      lower      upper 
## -1.3709646 -0.4446533

t_test(at_no.outliers, re_diff.mp.hp ~ group)

## # A tibble: 1 x 8
##   .y.           group1 group2    n1    n2 statistic    df      p
## * <chr>         <chr>  <chr>  <int> <int>     <dbl> <dbl>  <dbl>
## 1 re_diff.mp.hp at     cg        41    39     -2.00  76.9 0.0489

cohen.d(re_diff.mp.hp ~ group, at_no.outliers, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.4414623 (small)
## 95 percent confidence interval:
##        lower        upper 
## -0.887808973  0.004884379

Mental effort and movement reinvestment difference scores (low- minus high-pressure post-test) were calculated to serve as mediating variables in mediation analyses.

at_no.outliers$men_eff.diff.lp.hp = (at_no.outliers$men.eff_hp - at_no.outliers$men.eff_lp)

at_no.outliers$rein.diff.lp.hp = (at_no.outliers$rein_hp - at_no.outliers$rein_lp)

The models for each path in the mediation analyses were created.

Path c

path_c.model = lm(re_diff.lp.hp ~ group_dummy, at_no.outliers)

summary(path_c.model)

## 
## Call:
## lm(formula = re_diff.lp.hp ~ group_dummy, data = at_no.outliers)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.913  -9.478  -1.318   9.766  48.077 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    11.418      2.798   4.081 0.000107 ***
## group_dummy1  -16.015      3.908  -4.098 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.47 on 78 degrees of freedom
## Multiple R-squared:  0.1772, Adjusted R-squared:  0.1666 
## F-statistic: 16.79 on 1 and 78 DF,  p-value: 0.0001012

Path a for mental effort

path_a.men.eff.model = lm(men_eff.diff.lp.hp ~ group_dummy, at_no.outliers)

summary(path_a.men.eff.model)

## 
## Call:
## lm(formula = men_eff.diff.lp.hp ~ group_dummy, data = at_no.outliers)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -27.923 -11.505  -2.923   6.634  41.634 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    22.923      2.545   9.009 1.04e-13 ***
## group_dummy1   -9.557      3.554  -2.689  0.00876 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.89 on 78 degrees of freedom
## Multiple R-squared:  0.08483,    Adjusted R-squared:  0.0731 
## F-statistic:  7.23 on 1 and 78 DF,  p-value: 0.008764

Path a for movement reinvestment

path_a.rein.model = lm(rein.diff.lp.hp ~ group_dummy, at_no.outliers)

summary(path_a.rein.model)

## 
## Call:
## lm(formula = rein.diff.lp.hp ~ group_dummy, data = at_no.outliers)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3675 -0.3675 -0.1870  0.1463  2.4658 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.5342     0.1085   4.924 4.64e-06 ***
## group_dummy1  -0.3472     0.1515  -2.291   0.0246 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6775 on 78 degrees of freedom
## Multiple R-squared:  0.06306,    Adjusted R-squared:  0.05105 
## F-statistic:  5.25 on 1 and 78 DF,  p-value: 0.02465

Path b for mental effort

path_b.men.eff.model = lm(re_diff.lp.hp ~ group_dummy + men_eff.diff.lp.hp, at_no.outliers)

summary(path_b.men.eff.model)

## 
## Call:
## lm(formula = re_diff.lp.hp ~ group_dummy + men_eff.diff.lp.hp, 
##     data = at_no.outliers)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.541  -9.023  -1.117   8.462  47.888 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         12.70275    4.01692   3.162  0.00224 ** 
## group_dummy1       -16.55059    4.10611  -4.031  0.00013 ***
## men_eff.diff.lp.hp  -0.05604    0.12513  -0.448  0.65554    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.56 on 77 degrees of freedom
## Multiple R-squared:  0.1793, Adjusted R-squared:  0.158 
## F-statistic: 8.411 on 2 and 77 DF,  p-value: 0.0004966

Path b results indicated that the mental effort difference score did not explain the radial error difference score, so mental effort did not mediate the relationship between group and radial error difference score.

Path b for movement reinvestment

path_b.rein.model = lm(re_diff.lp.hp ~ group_dummy + rein.diff.lp.hp, at_no.outliers)

summary(path_b.rein.model)

## 
## Call:
## lm(formula = re_diff.lp.hp ~ group_dummy + rein.diff.lp.hp, data = at_no.outliers)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.690  -9.352  -1.244   9.938  48.195 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      11.0813     3.2229   3.438 0.000947 ***
## group_dummy1    -15.7961     4.0622  -3.889 0.000212 ***
## rein.diff.lp.hp   0.6307     2.9381   0.215 0.830609    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.58 on 77 degrees of freedom
## Multiple R-squared:  0.1777, Adjusted R-squared:  0.1563 
## F-statistic: 8.318 on 2 and 77 DF,  p-value: 0.0005364

Path b results indicate that the movement reinvestment difference score did not explain the radial error difference score, so movement reinvestment did not mediate the relationship between group and radial error difference score.

Scatterplots of the variables in the mediation analyses were examined to test the linear regression assumption of linearity. (Note that a column to make group names was added.)

at_no.outliers$group_name <- with(at_no.outliers, ifelse(group=="at","Anxiety Training","Control"))

at_no.outliers %>%
  ggplot(aes(x = `men_eff.diff.lp.hp`, y = `re_diff.lp.hp`, color = group_name)) +
  geom_point() + 
  geom_smooth(method = lm)+
  scale_x_continuous(name = "Mental Effort LP - HP") +
  scale_y_continuous(name = "Radial Error LP - HP (cm)") +
  theme(legend.position = "top") +
  guides(color = guide_legend(title = "Group"))

ggsave(here("output", "re_men.eff_group.png"))

at_no.outliers %>%
  ggplot(aes(x = `rein.diff.lp.hp`, y = `re_diff.lp.hp`, color = group_name)) +
  geom_point() + 
  geom_smooth(method = lm)+
  scale_x_continuous(name = "Movement Reinvestment LP - HP") +
  scale_y_continuous(name = "Radial Error LP - HP (cm)") +
  theme(legend.position = "top") +
  guides(color = guide_legend(title = "Group"))

ggsave(here("output", "re_rein_group.png"))

Scatterplots of the residuals versus the predicted values for the variables in the mediation analyses were examined to test the linear regression assumptions of independence of errors and homoscedasticity. Normal probability plots for the variables in the mediation analyses were examined to test the linear regression assumption of normality of errors.

plot(path_b.men.eff.model)

plot(path_b.rein.model)

Variance inflation factors for the variables in the mediation analyses were examined to test the linear regression assumption of non-multicollinearity.

car::vif(path_b.men.eff.model)

##        group_dummy men_eff.diff.lp.hp 
##           1.092691           1.092691

car::vif(path_b.rein.model)

##     group_dummy rein.diff.lp.hp 
##        1.067304        1.067304

Practice analyses

A practice data frame with separate factors of day and block for putting and heart rate was created.

at_no.outliers.putt.heart.practice <- select(at_no.outliers.putt.heart, id, group, re_d01.e:re_d02.l, hr_d01.e:hr_d02.l)

at_no.outliers.putt.heart.practice.long <- at_no.outliers.putt.heart.practice %>%
  pivot_longer(
    !id & !group, 
    names_to = c(".value","phase"),
    names_sep = "_")

at_no.outliers.putt.heart.practice.long$day <- with(at_no.outliers.putt.heart.practice.long, ifelse(phase=="d01.e"|phase=="d01.m"|phase=="d01.l",01,02))

at_no.outliers.putt.heart.practice.long = at_no.outliers.putt.heart.practice.long %>% mutate(block = 
                                                                        case_when(
phase == "d01.e"~"e",
phase == "d02.e"~"e",
phase == "d01.m"~"m",                                                     phase == "d02.m"~"m",                                                     phase == "d01.l"~"l",
phase == "d02.l"~"l"))

Putting accuracy

re_practice.model.no.outliers <- aov_ez("id","re", at_no.outliers.putt.heart.practice.long, between = "group", within = c("day", "block"), anova_table = list(es = "pes"))

summary(re_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                  Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept)     1408962      1    72363     78 1518.7119 < 2.2e-16 ***
## group              2217      1    72363     78    2.3898    0.1262    
## day               12659      1    29738     78   33.2031 1.578e-07 ***
## group:day            32      1    29738     78    0.0839    0.7728    
## block             28379      2    36509    156   60.6309 < 2.2e-16 ***
## group:block         656      2    36509    156    1.4025    0.2491    
## day:block           538      2    37931    156    1.1071    0.3331    
## group:day:block     128      2    37931    156    0.2639    0.7684    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                 Test statistic  p-value
## block                  0.80047 0.000190
## group:block            0.80047 0.000190
## day:block              0.92451 0.048711
## group:day:block        0.92451 0.048711
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                  GG eps Pr(>F[GG])    
## block           0.83366     <2e-16 ***
## group:block     0.83366     0.2490    
## day:block       0.92981     0.3300    
## group:day:block 0.92981     0.7524    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                    HF eps   Pr(>F[HF])
## block           0.8496866 1.509472e-17
## group:block     0.8496866 2.491281e-01
## day:block       0.9515976 3.309934e-01
## group:day:block 0.9515976 7.575140e-01

knitr::kable(nice(re_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	927.73	2.39	.030	.126
day	1, 78	381.25	33.20 ***	.299	<.001
group:day	1, 78	381.25	0.08	.001	.773
block	1.67, 130.05	280.73	60.63 ***	.437	<.001
group:block	1.67, 130.05	280.73	1.40	.018	.249
day:block	1.86, 145.05	261.50	1.11	.014	.330
group:day:block	1.86, 145.05	261.50	0.26	.003	.752

Heart rate

hr_practice.model.no.outliers <- aov_ez("id","hr", at_no.outliers.putt.heart.practice.long, between = "group", within = c("day", "block"), anova_table = list(es = "pes"))

summary(hr_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##                  Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept)     3465810      1    53757     71 4577.4573 < 2.2e-16 ***
## group                15      1    53757     71    0.0201  0.887530    
## day                 231      1    21743     71    0.7548  0.387882    
## group:day           373      1    21743     71    1.2170  0.273683    
## block               171      2     2327    142    5.2054  0.006582 ** 
## group:block          73      2     2327    142    2.2356  0.110680    
## day:block            11      2     1487    142    0.5268  0.591632    
## group:day:block      13      2     1487    142    0.6148  0.542171    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##                 Test statistic    p-value
## block                  0.68242 1.5560e-06
## group:block            0.68242 1.5560e-06
## day:block              0.76107 7.0758e-05
## group:day:block        0.76107 7.0758e-05
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##                  GG eps Pr(>F[GG])  
## block           0.75897    0.01264 *
## group:block     0.75897    0.12483  
## day:block       0.80715    0.55365  
## group:day:block 0.80715    0.50889  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                    HF eps Pr(>F[HF])
## block           0.7720816 0.01219913
## group:block     0.7720816 0.12405327
## day:block       0.8231445 0.55711230
## group:day:block 0.8231445 0.51192565

knitr::kable(nice(hr_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 71	757.15	0.02	<.001	.888
day	1, 71	306.24	0.75	.011	.388
group:day	1, 71	306.24	1.22	.017	.274
block	1.52, 107.77	21.59	5.21 *	.068	.013
group:block	1.52, 107.77	21.59	2.24	.031	.125
day:block	1.61, 114.61	12.98	0.53	.007	.554
group:day:block	1.61, 114.61	12.98	0.61	.009	.509

Mental effort

men.eff_practice.model.no.outliers <- aov_ez("id","men.eff", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "d01" | phase == "d02"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(men.eff_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 885653      1   122413     78 564.3262 < 2.2e-16 ***
## group         5905      1   122413     78   3.7626   0.05603 .  
## phase         2365      1     6345     78  29.0734 7.214e-07 ***
## group:phase      4      1     6345     78   0.0544   0.81619    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(men.eff_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	1569.40	3.76 +	.046	.056
phase	1, 78	81.35	29.07 ***	.272	<.001
group:phase	1, 78	81.35	0.05	<.001	.816

Movement reinvestment

rein_practice.model.no.outliers <- aov_ez("id","rein", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "d01" | phase == "d02"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(rein_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 2411.54      1   75.899     78 2478.2961 < 2.2e-16 ***
## group          2.25      1   75.899     78    2.3090    0.1327    
## phase          5.04      1   10.820     78   36.3312 5.197e-08 ***
## group:phase    0.09      1   10.820     78    0.6467    0.4237    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(rein_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.97	2.31	.029	.133
phase	1, 78	0.14	36.33 ***	.318	<.001
group:phase	1, 78	0.14	0.65	.008	.424

Challenge threat

ct_practice.model.no.outliers <- aov_ez("id","ct", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "d01" | phase == "d02"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(ct_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 906.09      1   418.37     78 168.9316 < 2.2e-16 ***
## group        53.99      1   418.37     78  10.0659 0.0021611 ** 
## phase         9.96      1    47.15     78  16.4779 0.0001161 ***
## group:phase   0.00      1    47.15     78   0.0058 0.9395576    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(ct_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	5.36	10.07 **	.114	.002
phase	1, 78	0.60	16.48 ***	.174	<.001
group:phase	1, 78	0.60	0.01	<.001	.940

Cognitive anxiety

cog.anx_practice.model.no.outliers <- aov_ez("id","cog.anx", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "d01" | phase == "d02"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(cog.anx_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 502.20      1   52.856     78 741.0942 < 2.2e-16 ***
## group         0.61      1   52.856     78   0.9054 0.3442668    
## phase         1.45      1    8.446     78  13.4226 0.0004513 ***
## group:phase   0.21      1    8.446     78   1.9529 0.1662370    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(cog.anx_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.68	0.91	.011	.344
phase	1, 78	0.11	13.42 ***	.147	<.001
group:phase	1, 78	0.11	1.95	.024	.166

Somatic anxiety

som.anx_practice.model.no.outliers <- aov_ez("id","som.anx", at_no.outliers.quest.long %>% filter(at_no.outliers.quest.long$phase == "d01" | phase == "d02"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(som.anx_practice.model.no.outliers)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##              Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 273.382      1  14.5763     78 1462.9157 < 2.2e-16 ***
## group         2.548      1  14.5763     78   13.6360 0.0004096 ***
## phase         1.334      1   5.6324     78   18.4790 4.916e-05 ***
## group:phase   0.580      1   5.6324     78    8.0292 0.0058568 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

knitr::kable(nice(som.anx_practice.model.no.outliers), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 78	0.19	13.64 ***	.149	<.001
phase	1, 78	0.07	18.48 ***	.192	<.001
group:phase	1, 78	0.07	8.03 **	.093	.006

The Group x Day interaction was followed up with an independent t-test of group differences on Day 2 only, because, from the group manipulation check, it was known that the groups differed on Day 1. The t-test deviates from analysis plan and was done at the recommendation of an anonymous reviewer.

t.test(som.anx ~ group, at_no.outliers.quest.long %>% 
         filter(at_no.outliers.quest.long$phase == "d02"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  som.anx by group
## t = 1.7675, df = 56.352, p-value = 0.08257
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -0.01759501  0.28168864
## sample estimates:
## mean in group at mean in group cg 
##         1.282230         1.150183

Sensitivity analyses

Excluding participants who did not follow pre-experiment instructions for Day 3

re_posttest.model.fail.instruct <- aov_ez("id","re", at_fail.instruct.putt.heart.long %>% filter(at_fail.instruct.putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(re_posttest.model.fail.instruct)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 388142      1    22822     61 1037.4304 < 2.2e-16 ***
## group          740      1    22822     61    1.9788 0.1645891    
## phase          321      2    16622    122    1.1786 0.3111783    
## group:phase   2252      2    16622    122    8.2629 0.0004311 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic   p-value
## phase              0.81742 0.0023625
## group:phase        0.81742 0.0023625
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.84561  0.3058372    
## group:phase 0.84561  0.0009452 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.8671192 0.3067106595
## group:phase 0.8671192 0.0008470777

knitr::kable(nice(re_posttest.model.fail.instruct), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 61	374.14	1.98	.031	.165
phase	1.69, 103.16	161.12	1.18	.019	.306
group:phase	1.69, 103.16	161.12	8.26 ***	.119	<.001

The Group x Post-test interaction was significant, so separate ANOVAs (post-test) were conducted for each group.

AT group

re_post.model.fail.instruct.at <- aov_ez("id", "re", at_fail.instruct.putt.heart.long %>% filter(at_fail.instruct.putt.heart.long$group == "at", at_fail.instruct.putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.fail.instruct.at)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value Pr(>F)    
## (Intercept) 192790      1   9617.0     33 661.5439 <2e-16 ***
## phase          484      2   9884.2     66   1.6147 0.2067    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic p-value
## phase        0.87755 0.12369
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])
## phase 0.89091     0.2096
## 
##          HF eps Pr(>F[HF])
## phase 0.9382636  0.2083816

knitr::kable(nice(re_post.model.fail.instruct.at), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.78, 58.80	168.10	1.61	.047	.210

Control group

re_post.model.fail.instruct.cg <- aov_ez("id", "re", at_fail.instruct.putt.heart.long %>% filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.fail.instruct.cg)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value    Pr(>F)    
## (Intercept) 195849      1  13205.4     28 415.2682 < 2.2e-16 ***
## phase         1971      2   6737.5     56   8.1913 0.0007577 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic   p-value
## phase        0.70177 0.0083867
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])   
## phase 0.77028   0.002209 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps Pr(>F[HF])
## phase 0.8064429 0.00186555

knitr::kable(nice(re_post.model.fail.instruct.cg), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.54, 43.14	156.19	8.19 **	.226	.002

There was a significant effect of post-test for the control group, so paired t-tests were conducted between each pair of post-tests. A Bonferonni correction should be applied to the p-values below. The two-tailed (as opposed to one-tailed) t-tests and Bonferroni corrections (as opposed to no corrections) deviate from analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(re ~ phase, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = -3.1153, df = 28, p-value = 0.004215
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -10.026313  -2.071618
## sample estimates:
## mean of the differences 
##               -6.048966

t.test(re ~ phase, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "lp" | phase == "hp"),paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = 3.6151, df = 28, p-value = 0.001167
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   5.051451 18.260963
## sample estimates:
## mean of the differences 
##                11.65621

t.test(re ~ phase, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = 1.7121, df = 28, p-value = 0.09793
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.101328 12.315810
## sample estimates:
## mean of the differences 
##                5.607241

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(re ~ phase, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.3775796 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.6288781 -0.1262811

cohen.d(re ~ phase, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.7370298 (medium)
## 95 percent confidence interval:
##     lower     upper 
## 0.2764787 1.1975809

cohen.d(re ~ phase, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$group == "cg", at_fail.instruct.putt.heart.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.3165861 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.06299749  0.69616963

t.test(re ~ group, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$phase == "lp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = 1.4609, df = 60.997, p-value = 0.1492
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -1.629096 10.464836
## sample estimates:
## mean in group at mean in group cg 
##         45.96235         41.54448

t.test(re ~ group, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$phase == "mp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = -0.9874, df = 54.92, p-value = 0.3278
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -11.479554   3.901481
## sample estimates:
## mean in group at mean in group cg 
##         43.80441         47.59345

t.test(re ~ group, at_fail.instruct.putt.heart.long %>% 
         filter(at_fail.instruct.putt.heart.long$phase == "hp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = -2.9503, df = 55.279, p-value = 0.004648
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -21.059729  -4.023416
## sample estimates:
## mean in group at mean in group cg 
##         40.65912         53.20069

Effect sizes were calculated for the two-sample t-tests.

cohen.d(re_lp ~ group, at_fail.instruct, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.3598514 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.1433595  0.8630622

cohen.d(re_mp ~ group, at_fail.instruct, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.2499879 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.7511338  0.2511579

cohen.d(re_hp ~ group, at_fail.instruct, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.7462604 (medium)
## 95 percent confidence interval:
##      lower      upper 
## -1.2624501 -0.2300707

Outliers included

re_posttest.model <- aov_ez("id","re", at_putt.heart.long %>% filter(at_putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), between = "group", within = "phase", anova_table = list(es = "pes"))

summary(re_posttest.model)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df   F value    Pr(>F)    
## (Intercept) 550259      1    37365     82 1207.5758 < 2.2e-16 ***
## group         1272      1    37365     82    2.7924   0.09852 .  
## phase         1121      2    33415    164    2.7506   0.06684 .  
## group:phase   4982      2    33415    164   12.2258 1.124e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##             Test statistic  p-value
## phase              0.91415 0.026374
## group:phase        0.91415 0.026374
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##              GG eps Pr(>F[GG])    
## phase       0.92094    0.07156 .  
## group:phase 0.92094  2.181e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                HF eps   Pr(>F[HF])
## phase       0.9411109 7.032517e-02
## group:phase 0.9411109 1.841307e-05

knitr::kable(nice(re_posttest.model), "pipe")

Effect	df	MSE	F	pes	p.value
group	1, 82	455.67	2.79 +	.033	.099
phase	1.84, 151.03	221.24	2.75 +	.032	.072
group:phase	1.84, 151.03	221.24	12.23 ***	.130	<.001

The Group x Post-test interaction was significant, so separate ANOVAs (post-test) were conducted for each group.

AT group

re_post.model.at <- aov_ez("id", "re", at_putt.heart.long %>% filter(at_putt.heart.long$group == "at", at_putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.at)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df  F value Pr(>F)    
## (Intercept) 249305      1    13509     41 756.6629 <2e-16 ***
## phase          689      2    14576     82   1.9373 0.1506    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic p-value
## phase        0.95569 0.40396
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])
## phase 0.95757     0.1527
## 
##         HF eps Pr(>F[HF])
## phase 1.003405  0.1506315

knitr::kable(nice(re_post.model.at), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.92, 78.52	185.64	1.94	.045	.153

Control group

re_post.model.cg <- aov_ez("id", "re", at_putt.heart.long %>% filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "lp" | phase =="mp" | phase == "hp"), within = "phase", anova_table = list(es = "pes"))

summary(re_post.model.cg)

## 
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
## 
##             Sum Sq num Df Error SS den Df F value    Pr(>F)    
## (Intercept) 302226      1    23857     41 519.409 < 2.2e-16 ***
## phase         5414      2    18839     82  11.783 3.176e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Mauchly Tests for Sphericity
## 
##       Test statistic  p-value
## phase        0.85083 0.039523
## 
## 
## Greenhouse-Geisser and Huynh-Feldt Corrections
##  for Departure from Sphericity
## 
##        GG eps Pr(>F[GG])    
## phase 0.87019  8.398e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##          HF eps   Pr(>F[HF])
## phase 0.9054624 6.445584e-05

knitr::kable(nice(re_post.model.cg), "pipe")

Effect	df	MSE	F	pes	p.value
phase	1.74, 71.36	264.01	11.78 ***	.223	<.001

There was a significant effect of post-test for the control group, so paired t-tests were conducted between each pair of post-tests. A Bonferonni correction should be applied to the p-values below. The two-tailed (as opposed to one-tailed) t-tests and Bonferroni corrections (as opposed to no corrections) deviate from analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(re ~ phase, at_putt.heart.long %>% 
         filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "lp" | phase == "mp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = -3.4725, df = 41, p-value = 0.00123
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -15.297706  -4.047056
## sample estimates:
## mean of the differences 
##               -9.672381

t.test(re ~ phase, at_putt.heart.long %>% 
         filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "lp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = 4.1229, df = 41, p-value = 0.0001777
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   8.129796 23.741157
## sample estimates:
## mean of the differences 
##                15.93548

t.test(re ~ phase, at_putt.heart.long %>% 
         filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "mp" | phase == "hp"), paired = TRUE)

## 
##  Paired t-test
## 
## data:  re by phase
## t = 1.9686, df = 41, p-value = 0.05579
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.1622013 12.6883918
## sample estimates:
## mean of the differences 
##                6.263095

Effect sizes were calculated for the paired-sample t-tests.

cohen.d(re ~ phase, at_putt.heart.long %>% 
         filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "lp" |    phase == "mp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.5547576 (medium)
## 95 percent confidence interval:
##      lower      upper 
## -0.8961462 -0.2133690

cohen.d(re ~ phase, at_putt.heart.long %>% 
         filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "lp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.873133 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.3780215 1.3682445

cohen.d(re ~ phase, at_putt.heart.long %>% 
         filter(at_putt.heart.long$group == "cg", at_putt.heart.long$phase == "mp" |    phase == "hp"), paired=TRUE, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.2828469 (small)
## 95 percent confidence interval:
##        lower        upper 
## -0.008643439  0.574337210

Because of the significant Group x Post-test interaction, two-tailed t-tests were conducted between groups for each post-test, and a Bonferroni correction should be applied to the p-values below. The t-tests and Bonferroni correction deviate from analysis plan and were done at the recommendation of an anonymous reviewer.

t.test(re ~ group, at_putt.heart.long %>% 
         filter(at_putt.heart.long$phase == "lp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = 2.3915, df = 69.552, p-value = 0.01949
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##   1.180614 13.047957
## sample estimates:
## mean in group at mean in group cg 
##         47.55405         40.43976

t.test(re ~ group, at_putt.heart.long %>% 
         filter(at_putt.heart.long$phase == "mp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = -1.6179, df = 73.208, p-value = 0.11
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -13.633768   1.416149
## sample estimates:
## mean in group at mean in group cg 
##         44.00333         50.11214

t.test(re ~ group, at_putt.heart.long %>% 
         filter(at_putt.heart.long$phase == "hp"), paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  re by group
## t = -3.4151, df = 70.449, p-value = 0.001061
## alternative hypothesis: true difference in means between group at and group cg is not equal to 0
## 95 percent confidence interval:
##  -22.947836  -6.027878
## sample estimates:
## mean in group at mean in group cg 
##         41.88738         56.37524

Effect sizes were calculated for the two-sample t-tests.

cohen.d(re_lp ~ group, at, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: 0.5170886 (medium)
## 95 percent confidence interval:
##      lower      upper 
## 0.07983747 0.95433968

cohen.d(re_mp ~ group, at, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.349805 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.7832042  0.0835943

cohen.d(re_hp ~ group, at, hedges.correction=TRUE)

## 
## Hedges's g
## 
## g estimate: -0.7384043 (medium)
## 95 percent confidence interval:
##     lower     upper 
## -1.182942 -0.293866

Tables

Cognitive anxiety

apa.2way.table(
  group,
  phase,
  cog.anx,
  at_no.outliers.quest.fig.long,
  filename = "cog.anx_table.docx")

## 
## 
## Means and standard deviations for cog.anx as a function of a 2(group) X 6(phase) design 
## 
##        phase                                                       
##          d01       d02        hp        lp        mp       pre     
##  group     M   SD    M   SD    M   SD    M   SD    M   SD    M   SD
##     at  1.97 0.59 1.70 0.57 2.24 0.71 1.66 0.56 1.83 0.59 1.80 0.58
##     cg  1.77 0.68 1.65 0.66 2.31 0.77 1.64 0.61 2.02 0.78 1.89 0.65
## 
## Note. M and SD represent mean and standard deviation, respectively.

Somatic anxiety

apa.2way.table(
  group,
  phase,
  som.anx,
  at_no.outliers.quest.fig.long,
  filename = "som.anx_table.doc")

## 
## 
## Means and standard deviations for som.anx as a function of a 2(group) X 6(phase) design 
## 
##        phase                                                       
##          d01       d02        hp        lp        mp       pre     
##  group     M   SD    M   SD    M   SD    M   SD    M   SD    M   SD
##     at  1.59 0.44 1.28 0.43 1.50 0.49 1.18 0.30 1.24 0.39 1.43 0.38
##     cg  1.21 0.30 1.15 0.20 1.56 0.56 1.13 0.22 1.34 0.42 1.26 0.32
## 
## Note. M and SD represent mean and standard deviation, respectively.

Heart rate

apa.2way.table(
  group,
  phase,
  hr,
  at_no.outliers.putt.heart.fig.long,
  filename = "hr_table.doc")

## 
## 
## Means and standard deviations for hr as a function of a 2(group) X 10(phase) design 
## 
##        phase                                                                  
##        d01.e       d01.l       d01.m       d02.e       d02.l       d02.m      
##  group     M    SD     M    SD     M    SD     M    SD     M    SD     M    SD
##     at 88.03 13.86 89.24 13.16 89.09 13.07 90.77 13.57 90.35 12.91 90.91 13.45
##     cg 88.17 12.87 90.43 13.44 89.42 13.60 87.87 15.67 90.46 14.64 88.62 14.54
##                                                 
##     hp          lp          mp         pre      
##      M    SD     M    SD     M    SD     M    SD
##  89.82 16.00 85.70 15.86 86.78 15.66 88.91 15.61
##  91.68 12.65 88.90 11.98 89.66 11.65 88.86 14.20
## 
## Note. M and SD represent mean and standard deviation, respectively.

Self-confidence

apa.2way.table(
  group,
  phase,
  sc,
  at_no.outliers.quest.fig.long,
  filename = "sc_table.doc")

## 
## 
## Means and standard deviations for sc as a function of a 2(group) X 6(phase) design 
## 
##        phase                                                       
##          d01       d02        hp        lp        mp       pre     
##  group     M   SD    M   SD    M   SD    M   SD    M   SD    M   SD
##     at  2.74 0.62 2.71 0.64 2.68 0.73 2.66 0.75 2.58 0.76 2.63 0.63
##     cg  2.86 0.81 2.91 0.81 2.76 0.94 2.92 0.84 2.87 0.90 2.70 0.77
## 
## Note. M and SD represent mean and standard deviation, respectively.

Anxiety Training Efficacy and Mechanisms

Matt Miller

27-05-2023

Note

Load packages

Load data

Identify and remove outliers

Calculate z-scores for post-tests

Remove participants with z-scores > 3.00 or < -3.00

Consistency analyses

Cognitive anxiety

Pre-test

Day 1

Day 2

Low-pressure post-test

Mild-pressure post-test

High-pressure post-test

Somatic anxiety

Pre-test

Day 1

Day 2

Low-pressure post-test

Mild-pressure post-test

High-pressure post-test

Self-confidence

Pre-test

Day 1

Day 2

Low-pressure post-test

Mild-pressure post-test

High-pressure post-test

Movement reinvestment

Pre-test

Day 1

Day 2

Low-pressure post-test

Mild-pressure post-test

High-pressure post-test

Average cognitive anxiety items for each time point

Average somatic anxiety items for each time point

Average self-confidence items for each time point

Average movement reinvestment items for each time point

Calculate challenge-threat score for each time point

Identify participants who did not follow pre-experiment instructions for Day 3

Calculate difference in sleep on night before Day 3 from average of nights before Days 1 and 2

Remove participants who did not follow pre-experiment instructions for Day 3

Correlations between cognitive and somatic anxiety subscales at each time point

Data normality assessment and transformation (based on post-tests)

Radial error

Q-Q plots for radial error

Shapiro-Wilk tests for radial error

Cognitive anxiety

Q-Q plots for cognitive anxiety

Shapiro-Wilk tests for cognitive anxiety

Log and reverse log transformations of cognitive anxiety data

Q-Q plots of log and reverse log transformed cognitive anxiety data

Shapiro-Wilk tests of log and reverse log transformed cognitive anxiety data

Somatic anxiety

Q-Q plots for somatic anxiety

Shapiro-Wilk tests for cognitive anxiety

Log and reverse log transformations of somatic anxiety data

Q-Q plots of log and reverse log transformed somatic anxiety data

Shapiro-Wilk tests of log and reverse log transformed somatic anxiety data

Mental effort

Q-Q plots for mental effort

Shapiro-Wilk tests for mental effort

Movement reinvestment

Q-Q plots for movement reinvestment

Shapiro-Wilk tests for movement reinvestment

Log and reverse log transformations of movement reinvestment data

Q-Q plots of log and reverse log transformed movement reinvestment data

Shapiro-Wilk tests of log and reverse log transformed movement reinvestment data

Challenge-threat

Q-Q plots for challenge-threat

Shapiro-Wilk tests for challenge-threat

Log and reverse log transformations of challenge-threat data

Q-Q plots of log and reverse log transformed challenge-threat data

Shapiro-Wilk tests of log and reverse log transformed challenge-threat data

Self-confidence

Q-Q plots for self-confidence