Understanding Power Analysis with G*Power

Power analysis is a critical step in research design that allows researchers to determine the sample size needed to detect an effect of a given size with a specified degree of confidence. GPower is a widely-used software tool that helps perform this analysis efficiently. Below are three practical examples that illustrate how GPower can be used in different research contexts.

Example 1: Determining Sample Size for a T-Test

In a study investigating the effect of a new teaching method on student performance, a researcher wants to compare test scores between two groups: one using the new method and the other using the traditional approach. The researcher anticipates a medium effect size (Cohen’s d = 0.5) and desires a power of 0.80 (80% chance of detecting an effect if one exists) with a significance level of 0.05.

To use G*Power, the researcher selects the following parameters:

• Test family: t-tests
• Statistical test: Means: Difference between two independent means (two groups)
• Type of power analysis: A priori (compute required sample size)
• Effect size: 0.5
• α error probability: 0.05
• Power (1-β error probability): 0.80

After inputting these parameters, G*Power calculates the required total sample size, which is 64 participants (32 per group). This means the researcher needs to recruit 64 students to achieve the desired power for detecting the effect of the teaching method.

Notes

• If the researcher was interested in a larger effect size, the required sample size would decrease.
• Conversely, if a higher power level (e.g., 0.90) is desired, the sample size would increase.

Example 2: Power Analysis for ANOVA

A nutritionist is conducting an experiment to compare the effects of three different diets on weight loss. The diets are classified as Diet A, Diet B, and Diet C. The nutritionist expects a small to medium effect size (f = 0.25) and aims for a power of 0.85 with a significance level of 0.05.

Using G*Power, the parameters are set as follows:

• Test family: F-tests
• Statistical test: ANOVA: Fixed effects, omnibus, one-way
• Type of power analysis: A priori (compute required sample size)
• Effect size: 0.25
• α error probability: 0.05
• Power (1-β error probability): 0.85
• Number of groups: 3

G*Power calculates the required total sample size to be 78 participants (26 per group). This indicates that the nutritionist needs to recruit at least 78 individuals to ensure adequate power to detect differences among the three diets.

Notes

• If the number of groups increases, the required sample size also increases, assuming the same effect size and power.
• Researchers can conduct post-hoc power analysis in G*Power after data collection to evaluate the achieved power of their study.

Example 3: Chi-Square Test Power Analysis

A public health researcher wants to examine the relationship between smoking status (smoker, non-smoker) and the occurrence of a specific health condition (yes, no). To determine how many participants are needed to detect a significant association, the researcher anticipates a medium effect size (w = 0.3) with a desired power of 0.90 and an α level of 0.05.

In G*Power, the following settings are chosen:

• Test family: Chi-square tests
• Statistical test: Chi-square tests: Contingency tables (2x2)
• Type of power analysis: A priori (compute required sample size)
• Effect size: 0.3
• α error probability: 0.05
• Power (1-β error probability): 0.90

The output from G*Power shows that a total sample size of 88 participants is required (44 in each category of smoking status). This indicates that the researcher should aim to recruit at least 88 individuals to ensure a robust analysis of the relationship between smoking and health conditions.

Notes

• If the researcher had anticipated a larger effect size, the required sample size would be smaller.
• It’s essential to ensure that the sample size is feasible within the constraints of time and resources available for the study.