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(effectsize) #adding this to calculate eta squared!
# library(langcog) #95 percent confidence intervals - BUT not available for new version of R# Just Experiment 6
setwd("~/Desktop/problem_sets/ps3/GroupA/Choice3/data")
data <- read_excel("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_analysis <- d %>%
select(c(Subject,
Cond,
Slack,
Large,
tmest,
expense,
error)) %>% # including only columns we need
group_by(Cond) %>%
summarise(Avg = mean(expense),
sd_expense = sd(expense),
n_obs = length(expense),
sem = sd_expense / sqrt(n_obs),
ci = sem * 1.96,
ci_lower = Avg - ci,
ci_upper = Avg + ci)
d_analysis## # A tibble: 4 × 8
## Cond Avg sd_expense n_obs sem ci ci_lower ci_upper
## <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
## 1 0 8.33 2.78 21 0.607 1.19 7.14 9.52
## 2 1 8.31 1.08 16 0.270 0.528 7.78 8.84
## 3 2 8.83 1.86 18 0.437 0.857 7.98 9.69
## 4 3 6.5 2.33 18 0.550 1.08 5.42 7.58A 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
d_anova <- d %>%
select(c(Subject,
Cond,
Slack,
Large,
tmest,
expense,
error)) %>%
mutate(scarcity_cond = case_when(Cond == 0 | Cond == 2 ~ "time-poor",
Cond == 1 | Cond == 3 ~ "time-rich"),
account_cond = case_when(Cond == 0 | Cond == 1 ~ "small account",
Cond == 2 | Cond == 3 ~ "large account"))
scarcity_aov <- aov(expense ~ scarcity_cond * account_cond, data = d_anova)
summary(scarcity_aov) # got the same F statistic! ## Df Sum Sq Mean Sq F value Pr(>F)
## scarcity_cond 1 26.6 26.646 5.690 0.0198 *
## account_cond 1 6.1 6.078 1.298 0.2585
## scarcity_cond:account_cond 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 ' ' 1eta_squared(scarcity_aov, partial = TRUE) # it worked!## # Effect Size for ANOVA (Type I)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------------
## scarcity_cond | 0.08 | [0.01, 1.00]
## account_cond | 0.02 | [0.00, 1.00]
## scarcity_cond:account_cond | 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?
Yes, I was able to replicate the results.
How difficult was it to reproduce your results?
Not difficult at all. Pretty straightforward analysis. (#humble)
What aspects made it difficult? What aspects made it easy?
It was helpful that they already had the tidy data; I am sure that this would have been more frustrating to analyze if I had to clean up the data. In fact, the hardest aspect of this was trying to figure out what the label for the conditions meant (it was not explicit what Cond = 0 meant but it was necessary in order to run the anova). However, I think I was able to confirm the groups from the means I calculated and their summary paragraph provided (could be wrong! Open to feedback or if I missed materials where this was identified)