Track C – Chapter 20 Problem Set (Responsible Researcher)

This problem set practices the capstone ideas of a responsible researcher:

Power analysis (planning sample size before running a study)
Meta-analysis (combining evidence across studies)
Research integrity (how questionable practices inflate false positives)

Run the worked solutions

make psych-ch20-problems

Run only the tests

make test-psych-ch20-problems

Files and outputs

The solution script writes:

Synthetic datasets: data/synthetic/
Summaries + plots: outputs/track_c/

Exercises

Exercise 1 — Power analysis (a priori)

Plan a study to detect a moderate effect (Cohen’s d = 0.50) with:

alpha = 0.05 (two-sided)
target power = 0.80

You will interpret:

The required n per group
The power curve (power as a function of sample size)

Exercise 2 — Meta-analysis (fixed vs random)

You are given a set of simulated studies with heterogeneity.

You will interpret:

The fixed-effect pooled estimate
The random-effects pooled estimate
Heterogeneity statistics (Q, I², tau²)

Exercise 3 — Optional stopping inflates Type I error

A researcher “peeks” at the p-value multiple times and stops early if p < 0.05. Even if the null hypothesis is true, this practice inflates false positives.

You will interpret:

The observed false-positive rate
Why “peeking” violates the planned alpha level