Problem set 2

Task 1: Hypothesis testing

We consider the hypothesis test performed by Bastian et al. (2014) with the data they collected in their Experiment 1. The R and SPSS files containing code for performing the testing procedures and extracting the output are provided. You can also download the SPSS data file and the paper via OpenStats Lab.

  1. Briefly comment on the generalisability of the study in light of the sample composition and data collection.
  2. The authors used a two-sample t-test to assess the hypothesis that people in the pain condition felt more threatened by the tasks (a manipulation check). One criticism of using such a test statistic is that it assumes that observations in both group have potentially different group average, but similar standard deviation.1 An alternative test which doesn’t assume equal variance in each experimental condition is Welch’s t-test. Use the latter instead to model the manipulation check for threat and report the output. Do the conclusions change?
  3. The authors report results based on a one-way analysis of variance, a testing procedure that compares the mean of \(m\) different groups. The latter is equivalent to a two-sample t-test when there are only \(m=2\) groups.
    1. Using the two-sample t-test, obtain a 95% and a 99% confidence interval for the mean difference score for perceived bonding.
    2. Explain how the two methods (p-value and confidence intervals) are equivalent for performing an hypothesis test with a significance level of 5% and 1%, respectively. Report the conclusions of your procedure in each case.
    3. List an advantage of each over the other.
  4. Extract the degrees of freedom, the value of the \(F\)-statistic and the p-value, suitably rounded, and report these.
  5. What can we reasonably conclude about the effect of bonding based on the output of the testing procedure? Is this reflected in the writing of the authors?
  6. Figure 1 of Bastian et al. (2014) shows a dynamite plot, i.e., a bar plot with 95% confidence intervals for each condition. Note that this is standard display, but overall it is poor graphical choice (why?). Briefly summarize the blog post.

Task 2 - Reproducibility

Section 3.2 of Duke & Amir (2023) report the results of an online experiment (Experiment 1) and the impact on sales of sequential vs integrated decision making; the data can be found in the R package hecedsm under DA23_E1; you can also download the SPSS database.

Reproduce the results reported in Section 3.2.2 and check that your results match those of the paper. Submit your code alongside your report.


Bastian, B., Jetten, J., & Ferris, L. J. (2014). Pain as social glue: Shared pain increases cooperation. Psychological Science, 25(11), 2079–2085.
Duke, K. E., & Amir, O. (2023). The importance of selling formats: When integrating purchase and quantity decisions increases sales. Marketing Science, 42(1), 87–109.


  1. We will see modelling assumptions in Week 3, take my word on it for now.↩︎