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
library(effectsize) # to calculate partial eta squared
# #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
## Step 1 - To produce the mean
descriptive_table = d %>%
# group by condition
group_by(Cond) %>%
# create the mean
summarise(mean = mean(expense, na.rm = T),
sd = sd(expense, na.rm = T))
print(descriptive_table)## # A tibble: 4 × 3
## Cond mean sd
## <dbl> <dbl> <dbl>
## 1 0 8.33 2.78
## 2 1 8.31 1.08
## 3 2 8.83 1.86
## 4 3 6.5 2.33## Step 2 - Add confidence intervals
t_value = qt(0.975, df = 72) # to calculate the t-value when 72 df (n)
# Add 95% confidence intervals
descriptive_table %>%
mutate(stand_error = sd/sqrt(73),
CI_low = mean - (t_value * stand_error),
CI_high = mean + (t_value * stand_error)
)## # A tibble: 4 × 6
## Cond mean sd stand_error CI_low CI_high
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 8.33 2.78 0.325 7.68 8.98
## 2 1 8.31 1.08 0.126 8.06 8.56
## 3 2 8.83 1.86 0.217 8.40 9.27
## 4 3 6.5 2.33 0.273 5.96 7.04A 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
# Regress expense (DV) on Slack condition, Large condition, and Slack x Large interaction
fit = lm(expense ~ Slack + Large + Slack*Large, data = d)
# Print using anova()
fit %>%
anova() # F(1, 69) = 5.16, p = .026## Analysis of Variance Table
##
## Response: expense
## Df Sum Sq Mean Sq F value Pr(>F)
## Slack 1 26.65 26.6456 5.6902 0.01981 *
## Large 1 6.08 6.0779 1.2980 0.25853
## Slack:Large 1 24.17 24.1724 5.1621 0.02621 *
## Residuals 69 323.10 4.6827
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Calculate effect size
eta_squared(fit) # partial eta squared = .07## # 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 [1.00].Were you able to reproduce the results you attempted to reproduce? If not, what part(s) were you unable to reproduce?
Yes, I was able to reproduce all of the results except for the 95% CI. I tried calculating the manually and I rechecked my work several times, but I was still not able to get them correct.
How difficult was it to reproduce your results?
This analysis was not very difficult to reproduce. It was quite straightforward.
What aspects made it difficult? What aspects made it easy?
The only thing that was challenging was that the variables were not clearly labelled. As such, I had to work “backwards” from the descriptive statistics data that I calculated to infer what each of the variables meant.