Optimizing Sample Size in Multiple Regression Analyses: A Practical Guideline

If you’re planning a research study and need to know how many participants to include, it’s essential to perform a power analysis. This analysis helps you calculate the number of people you need to detect a meaningful effect in your study.

G*Power is a free, user-friendly tool that researchers often use to do this. In this article, we’ll walk through the steps of using G*Power for multiple regression studies, where you have one main outcome you want to predict (like grades or happiness) and several factors you think might influence it (like self-esteem, income, or study habits).

When to Use This Type of Analysis
The multiple regression test in G*Power is perfect for studies where:

1. You’re predicting an outcome using several factors (variables).
2. You want to see if these factors, when combined, have a significant impact on the outcome.
3. You need to decide on the right number of participants to detect a possible relationship.

For example, if you want to predict a student’s general weighted average (GWA) using different factors like self-esteem, study habits, and family income, a multiple regression analysis can tell you if these factors combined have a significant influence on GWA.

Example Research Scenarios and Power Analysis
Let’s look at some examples of how this works in practice.

Scenario 1: Predicting Academic Performance (GWA)
Suppose you’re researching high school students’ academic performance. You want to know if self-esteem, study habits, and family income can predict students’ general weighted average (GWA).

Here’s what each factor could look like:

• Outcome: General Weighted Average (GWA)
• Predictor Factors:
  • Self-Esteem: measured by a self-esteem survey
  • Study Habits: measured by weekly study hours
  • Family Income: measured in Pesos

To find the right number of participants, you would use G*Power (click to download: Windows, Mac) to perform a power analysis with the following settings:

1. Effect Size: Choose an expected effect size. Researchers commonly use a “medium” effect size of 0.15 if they expect a moderate relationship.
2. Significance Level (Alpha): Usually set to 0.05, which means there’s a 5% chance of finding a significant result by accident.
3. Power: A power level of 0.80 (or 80%) means you have an 80% chance of detecting a true effect.
4. Number of Predictors: In this case, you have three predictors (self-esteem, study habits, and family income).

Result: G*Power shows that you need 77 students for this study. This sample size gives you a good chance of finding a real relationship if one exists between GWA and the combined predictors. The sample size determination may be reported in the methodology part of your research article (APA style) this way:

“An a priori power analysis was conducted using G*Power (Faul et al., 2009) to determine the minimum sample size required for a multiple regression analysis predicting General Weighted Average (GWA) based on self-esteem, study habits, and family income. Using a medium expected effect size (f² = 0.15), a significance level of α = 0.05, and a desired power of 0.80, with three predictor variables, the analysis indicated that a sample size of 77 participants would be sufficient to detect a significant relationship. This sample size was selected to ensure an 80% chance of identifying a real relationship if it exists among the predictor variables and GWA.”

Scenario 2: Predicting Job Satisfaction Based on Workplace Factors
Imagine a study where you want to predict employees’ job satisfaction (how happy they are with their job) based on factors like manager support, work-life balance, and salary.

Here’s how you could define these:

• Outcome: Job Satisfaction
• Predictor Factors:
  • Manager Support: rated on a scale
  • Work-Life Balance: satisfaction rating on a scale
  • Salary: in Pesos per month

This time, let’s assume you expect only a small effect because job satisfaction is affected by many factors outside of these three.

1. Effect Size: Set to 0.02, representing a small effect.
2. Significance Level (Alpha): 0.05
3. Power: Let’s use a higher power, 0.90 (90%), to make sure we have a strong chance of detecting a real effect.
4. Number of Predictors: 3

Result: G*Power suggests needing about 550 participants for this study. Because the effect is small, you need a larger sample size to detect it. The sample size determination may be reported in the methodology part of your research article (APA style) this way:

“To determine the necessary sample size for predicting job satisfaction from manager support, work-life balance, and salary, an a priori power analysis was conducted using G*Power (Faul et al., 2009). The analysis was set to detect a small effect size (f² = 0.02) with a significance level of α = 0.05 and a desired power of 0.90. Given three predictor variables, the analysis showed that a sample of approximately 550 participants would be needed to detect a statistically significant relationship with high confidence. This larger sample size was chosen to ensure a 90% chance of detecting a true relationship in the presence of a small effect.”

Scenario 3: Predicting Psychological Well-being Based on Lifestyle Factors
In this study, let’s say you want to understand the impact of lifestyle on psychological well-being (how happy and satisfied people feel) using factors like exercise, sleep quality, and social support.

Here’s how this could look:

• Outcome: Psychological Well-being
• Predictor Factors:
  • Exercise: hours per week
  • Sleep Quality: sleep quality score
  • Social Support: support score from friends/family

Since lifestyle factors often have a big impact on well-being, you expect a large effect for this study.

1. Effect Size: Set to 0.35 for a large effect.
2. Significance Level (Alpha): 0.05
3. Power: 0.80 (80%)
4. Number of Predictors: 3

Result: G*Power shows that 33 participants would be enough for this study. When you expect a large effect, fewer participants are required. The sample size determination may be reported in the methodology part of your research article (APA style) this way:

“An a priori power analysis was performed using G*Power (Faul et al., 2009) to determine the sample size needed to examine the effect of exercise, sleep quality, and social support on psychological well-being. Based on a large expected effect size (f² = 0.35), with a significance level of α = 0.05, a desired power of 0.80, and three predictor variables, the analysis indicated that a sample size of 33 participants would be adequate. This sample size was calculated to ensure an 80% chance of detecting a significant effect if one exists between lifestyle factors and psychological well-being.”

Key Points to Remember

1. Effect Size Matters: Smaller expected effects need larger sample sizes to detect them reliably, while large effects can be detected with fewer participants.
2. Power Level: A power level of 0.80 (or 80%) is common, but higher power (like 90%) may be used when you want even more confidence.
3. G*Power is Free and Easy to Use: You can download G*Power and practice power analysis for free. It’s a valuable tool for researchers!

Using power analysis not only helps you plan your study but also makes sure your research results are reliable and can be trusted. Whether you’re studying school performance, job satisfaction, or personal well-being, G*Power can guide you to the right sample size for your goals.

Reference

Faul, F., Erdfelder, E., Buchner, A., & Lang, A.G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods, 41(4), 1149-1160