Power Analysis for Mixed-Design ANOVA Examples

Explore practical examples of power analysis for mixed-design ANOVA.
By Jamie

In statistical research, power analysis is a vital tool that helps researchers determine the sample size required to detect an effect of a given size with a certain degree of confidence. Mixed-design ANOVA combines both between-subjects and within-subjects factors, making it essential to conduct a power analysis to ensure that the study is adequately powered. Below are three diverse, practical examples of power analysis for a mixed-design ANOVA.

Example 1: Evaluating the Effect of Teaching Methods on Student Performance

In an educational setting, a researcher seeks to understand how different teaching methods (e.g., traditional vs. interactive) affect student performance over two semesters. The study involves two between-subjects factors (teaching method) and one within-subjects factor (semester).

To conduct a power analysis, the researcher uses software to determine the necessary sample size. The following parameters are set:

  • Effect Size: Small (0.2)
  • Alpha Level: 0.05
  • Power: 0.80
  • Number of Groups: 2 (Teaching Method)
  • Number of Measurements: 2 (Semester)

Using these parameters, the power analysis reveals that a total sample size of 64 students (32 per teaching method) is needed to detect a significant interaction effect between teaching methods and semesters with 80% power.

Notes:

  • If the researcher expects a medium effect size (0.5), they can reduce the sample size to 34 students (17 per group).
  • The choice of effect size can substantially influence sample size requirements, so it’s crucial to base this on prior research or pilot studies.

Example 2: Investigating the Impact of Diet and Exercise on Weight Loss

A health researcher plans to investigate the effects of two different diets (low-carb vs. low-fat) and an exercise regimen (none vs. regular) on weight loss over three months. This study employs a mixed-design ANOVA with two between-subjects factors (diet and exercise) and one within-subjects factor (time).

The researcher performs a power analysis with the following parameters:

  • Effect Size: Medium (0.3)
  • Alpha Level: 0.05
  • Power: 0.90
  • Number of Groups: 4 (2 diets x 2 exercise regimens)
  • Number of Measurements: 3 (weeks 0, 6, and 12)

The results indicate that a total sample size of 120 participants is required (30 per group) to achieve a power of 90%.

Notes:

  • Increasing the power to 90% is beneficial for studies with significant health implications, where missing an effect could have real-world consequences.
  • Researchers should consider the feasibility of recruiting participants and the potential for dropouts when determining the final sample size.

Example 3: Assessing the Efficacy of a New Drug on Blood Pressure

In clinical research, a study aims to evaluate the effectiveness of a new drug in lowering blood pressure compared to a placebo. This study employs a mixed-design ANOVA with one between-subjects factor (drug vs. placebo) and one within-subjects factor (measurement time: baseline, 1 month, 3 months).

The power analysis is performed with these parameters:

  • Effect Size: Large (0.4)
  • Alpha Level: 0.01
  • Power: 0.85
  • Number of Groups: 2 (Drug and Placebo)
  • Number of Measurements: 3 (Time Points)

The analysis suggests that a sample size of 48 participants (24 per group) is sufficient to detect a significant difference in blood pressure with 85% power.

Notes:

  • A smaller alpha level (0.01) indicates a more stringent criterion for significance, which typically requires a larger sample size.
  • Researchers should also consider ethical implications when designing studies involving human subjects, ensuring they have enough power to justify their research without exposing participants to undue risk.