For this exercise, please try to reproduce the results from Experiment 6 of the associated paper (Shah, Shafir, & Mullainathan, 2015). The PDF of the paper is included in the same folder as this Rmd file.
The authors were interested in the effect of scarcity on people’s consistency of valuation judgments. In this study, participants played a game of Family Feud and were given either 75 s (budget - “poor” condition) or 250 s (budget - “rich” condition) to complete the game. After playing the game, participants were either primed to think about a small account of time necessary to play one round of the game (account -“small” condition) or a large account (their overall time budget to play the entire game, account - “large” condition.) Participants rated how costly it would feel to lose 10s of time to play the game. The researchers were primarily interested in an interaction between the between-subjects factors of scarcity and account, hypothesizing that those in the budget - “poor” condition would be more consistent in their valuation of the 10s regardless of account in comparison with those in the budget - “rich” condition. The authors tested this hypothesis with a 2x2 between-subjects ANOVA.
Below is the specific result you will attempt to reproduce (quoted directly from the results section of Experiment 6):
“One participant was excluded because of a computer malfunction during the game. Time-rich participants rated the loss as more expensive when they thought about a small account (M = 8.31, 95% CI = [7.78, 8.84]) than when they thought about a large account (M = 6.50, 95% CI = [5.42, 7.58]), whereas time-poor participants’ evaluations did not differ between the small-account condition (M = 8.33, 95% CI = [7.14, 9.52]) and the large account condition (M = 8.83, 95% CI = [7.97, 9.69]). A 2 (scarcity condition) × 2 (account condition) analysis of variance revealed a significant interaction, F(1, 69) = 5.16, p < .05, ηp2 = .07.” (Shah, Shafir & Mullainathan, 2015) ——
library(tidyverse) # for data munging
library(knitr) # for kable table formating
library(haven) # import and export 'SPSS', 'Stata' and 'SAS' Files
library(readxl) # import excel files
# #optional packages:
# library(afex) #anova functions
# library(langcog) #95 percent confidence intervals# Just Experiment 6
data <- read_excel("data/study 6-accessible-feud.xlsx")The data are already tidy as provided by the authors.
One participant was excluded because of a computer malfunction during the game (Shah, Shafir, & Mullainathan, 2015, p. 408)
Note: The original paper does not identify the participant that was excluded, but it was later revealed through communication with the authors that it was participant #16. The exclusion is performed below.
# Participant #16 should be dropped from analysis
excluded <- "16"
d <- data %>%
filter(!Subject %in% excluded) #participant exclusionsTime-rich participants rated the loss as more expensive when they thought about a small account (M = 8.31, 95% CI = [7.78, 8.84]) than when they thought about a large account (M = 6.50, 95% CI = [5.42, 7.58]), whereas time-poor participants’ evaluations did not differ between the small-account condition (M = 8.33, 95% CI = [7.14, 9.52]) and the large- account condition (M = 8.83, 95% CI = [7.97, 9.69]). (Shah, Shafir, & Mullainathan, 2015, p. 408)
# reproduce the above results here
d %>%
filter(Slack==1) %>%
group_by(Large) %>%
summarise(mean.exp = mean(expense, na.rm=T),
sd.exp = sd(expense, na.rm=T),
n.exp = n()) %>%
mutate(se.exp = sd.exp / sqrt(n.exp),
lower.ci.exp = mean.exp - qt(1 - (0.05/2), n.exp - 1)*se.exp,
upper.ci.exp = mean.exp + qt(1 - (0.05/2), n.exp - 1)*se.exp)## # A tibble: 2 x 7
## Large mean.exp sd.exp n.exp se.exp lower.ci.exp upper.ci.exp
## <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1 0 8.31 1.08 16 0.270 7.74 8.89
## 2 1 6.5 2.33 18 0.550 5.34 7.66d %>%
filter(Slack==0) %>%
group_by(Large) %>%
summarise(mean.exp = mean(expense, na.rm=T),
sd.exp = sd(expense, na.rm=T),
n.exp = n()) %>%
mutate(se.exp = sd.exp / sqrt(n.exp),
lower.ci.exp = mean.exp - qt(1 - (0.05/2), n.exp - 1)*se.exp,
upper.ci.exp = mean.exp + qt(1 - (0.05/2), n.exp - 1)*se.exp)## # A tibble: 2 x 7
## Large mean.exp sd.exp n.exp se.exp lower.ci.exp upper.ci.exp
## <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1 0 8.33 2.78 21 0.607 7.07 9.60
## 2 1 8.83 1.86 18 0.437 7.91 9.76A 2 (scarcity condition) × 2 (account condition) analysis of variance revealed a significant interaction, F(1, 69) = 5.16, p < .05, ηp2 = .07.
# reproduce the above results here
int <- aov(expense~Slack*Large, data = d)
summary(int)## Df Sum Sq Mean Sq F value Pr(>F)
## Slack 1 26.6 26.646 5.690 0.0198 *
## Large 1 6.1 6.078 1.298 0.2585
## Slack:Large 1 24.2 24.172 5.162 0.0262 *
## Residuals 69 323.1 4.683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(sjstats)
eta_sq(int, partial=T)## # Effect Size for ANOVA (Type I)
##
## Parameter | Eta2 (partial) | 95% CI
## -------------------------------------------
## Slack | 0.08 | [0.01, 1.00]
## Large | 0.02 | [0.00, 1.00]
## Slack:Large | 0.07 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at (1).Were you able to reproduce the results you attempted to reproduce? If not, what part(s) were you unable to reproduce?
Mostly. I was only unable to reproduce the exact 95% confidence interval for the means at 2 decimal places.
How difficult was it to reproduce your results?
Not too difficult.
What aspects made it difficult? What aspects made it easy?
I can’t imagine having to calculate partial eta sqaure by hand. So the additional package was handy for that purpose. Apart from that, I enjoyed the extra practice with tidyverse.