# 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.

- Briefly comment on the generalisability of the study in light of the sample composition and data collection.
- 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? - 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.- Using the two-sample
*t*-test, obtain a 95% and a 99% confidence interval for the mean difference score for perceived`bonding`

. - 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. - List an advantage of each over the other.

- Using the two-sample
- Extract the degrees of freedom, the value of the \(F\)-statistic and the
*p*-value, suitably rounded, and report these. - 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?
- 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.

## References

*Psychological Science*,

*25*(11), 2079–2085. https://doi.org/10.1177/0956797614545886

*Marketing Science*,

*42*(1), 87–109. https://doi.org/10.1287/mksc.2022.1364

## Footnotes

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