Replace “Your Name” with your actual name.

Learning Goals:

Learn to use the pwr package to calculate sample size or power for different types of psychological research designs.

Run the below chunk to load the pwr package.

library(pwr)

Exercise 1: Independent Samples t-Test

A psychologist is planning a study comparing two therapy conditions (CBT vs TAU) and expects a small/medium effect size (d = 0.32). They want 80% power and will use α = 0.05.

Instructions: Use pwr.t.test() to calculate the sample size needed per group. Interpret the result.

pwr.t.test(d = 0.32, power = 0.80, sig.level = 0.05,
           type = "two.sample")
## 
##      Two-sample t test power calculation 
## 
##               n = 154.2643
##               d = 0.32
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided
## 
## NOTE: n is number in *each* group

What is the minimum number of participants required per group? - We need 155 per group. Why is power important in this type of comparison? - It is important because we want to have enough power to detect a meaningful difference between the two groups.

Question 2: Correlation Study

You’re examining the correlation between mindfulness and stress in college students. Based on prior research, you expect a medium correlation of r = 0.3.

Instructions: Use pwr.r.test() to determine how many participants you need.

pwr.r.test(r = 0.3, power = 0.80, sig.level = 0.05)
## 
##      approximate correlation power calculation (arctangh transformation) 
## 
##               n = 84.07364
##               r = 0.3
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided

How many participants are needed? - We need 85 participants total. Why would correlational studies require more/less people than a t-test? - A correlation requires less because there are no groups to compare.

Question 3: Chi-Square Test

Suppose you’re comparing therapy outcomes across 4 different modalities (CBT, DBT, EMDR, TAU). You expect a medium effect size (w = 0.3).

Instructions: Run a power analysis using pwr.chisq.test(). You have a 4-group outcome variable with 1 binary outcome (e.g., success/failure), so df = (4-1)(2-1) = 3.

pwr.chisq.test(w = 0.30, df = 3, power = 0.80, sig.level = 0.05)
## 
##      Chi squared power calculation 
## 
##               w = 0.3
##               N = 121.1396
##              df = 3
##       sig.level = 0.05
##           power = 0.8
## 
## NOTE: N is the number of observations

What is the total number of participants needed? - We need a total of 122 participants. How does degrees of freedom affect the sample size? - The higher the degrees of freedom, the larger your sample size needs to be.

Question 4: Multiple Regression

You’re planning a study to predict depression scores using 5 predictors (e.g., sleep, diet, exercise, social support, and coping style). You expect a medium effect size (f² = 0.15).

Instructions: Use pwr.f2.test() to calculate the required sample size.

In the result, u is number of predictors, v is error degrees of freedom, so total n = u + v + 1

pwr.f2.test(u = 5, f2 = 0.15, power = 0.80, sig.level = 0.05)
## 
##      Multiple regression power calculation 
## 
##               u = 5
##               v = 85.21369
##              f2 = 0.15
##       sig.level = 0.05
##           power = 0.8
5 + 85.21369 + 1
## [1] 91.21369

What is the total number of participants you need? - 92 is the total sample size we need. Why do regression models require more people as you add more predictors? - Because we are asking our model to make more predictions.

Wrap-Up Questions. Answer these in your own words:

Why is power analysis important before conducting a study? - Power analysis helps you figure out how many participants you need to find a real effect. It prevents wasting resources or getting results that aren’t reliable.

Which design required the most participants? Why do you think that is? - Between-subjects designs usually need more participants because each group has different people, which adds more variability. More variability means you need a bigger sample to find differences.

Which test would be most efficient if you had limited resources? - A within-subjects test is most efficient because it uses the same people in all conditions. This reduces variability and needs fewer participants.

Submission Instructions:

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