Problem set 5

Complete this task individually

Submission information: please submit on ZoneCours

We consider data from Experiment 2 of Jordan et al. (2022), who measured the confidence of participants on their ability to land successfully a plane if the pilot was incapacitated, after they were exposed to a trivially uninformative 3 minute video of a pilot landing a plane, but filmed in such a way that it was utterly useless. The authors pre-registered a comparison between experimental conditions video vs no video, and found that people watching the video answered higher for the question “How confident are you that you would be able to land the plane without dying”, but there was no discernible effect for “How confident are you that you would be able to successfully land the plane as well as a pilot could”, contrary to expectations. They found that the order in which the questions were asked (order, either pilot first, or dying first) changed the response.

The database in package hecedsm in R is labelled JZBJG22_E2. You can also download the SPSS database via this link.

  1. A dataset is said to be balanced if there are the same number of people in each experimental condition. Are the data balanced over condition and order? Justify your answer.
  2. Plot the response variables using a suitable graph (e.g., half-violin or density plot), for each of the four conditions. Comment on the distribution of the scores along the scale.
  3. Using Levene’s test, check whether the variance in each subgroup is the same.
  4. Perform the two-way analysis of variance for both conf_dying and conf_pilot and report the null and alternative hypotheses, the test statistic, the \(P\)-value and the conclusion of the test. Use Welch’s ANOVA, i.e., an analysis of variance model with different variance for each subgroup if you rejected the null of homogeneity of variance in Question 3.
  5. For each response variable conf_dying and conf_pilot, perform follow-up tests. Compute simple or marginal effects (depending on whether the interaction is significant or not), along with 95% confidence intervals for the difference in score for video conditions.

Hint: to create a pretty plot in R, try the following:

# install.packages(c("ggplot2","ggdist"))
# remotes::install_github("lbelzile/hecedsm")
data(JZBJG22_E2, package = "hecedsm")
library(ggplot2)
library(ggdist)

ggplot(data = JZBJG22_E2, 
       mapping = aes(x = condition, group = order, y = conf_dying)) + 
  ggdist::stat_halfeye(adjust = .5, width = .3, .width = c(0.5, 1)) + 
  ggdist::stat_dots(side = "left", dotsize = .4, justification = 1.05, binwidth = .1) +
  facet_grid(~order) + 
  labs(y = "", subtitle = "confidence in landing without dying") +
  theme_classic()

References

Jordan, K., Zajac, R., Bernstein, D., Joshi, C., & Garry, M. (2022). Trivially informative semantic context inflates people’s confidence they can perform a highly complex skill. Royal Society Open Science, 9(3), 211977. https://doi.org/10.1098/rsos.211977