When planning a research study, especially one that looks at the relationship between two things, it’s important to choose the right number of people to include in the study. If the sample size (number of participants) is too small, it can be hard to see if there’s actually a relationship between the two variables you’re studying. But if the sample size is too large, you might waste time and resources. Tools like G*Power help researchers calculate the sample size they need to find meaningful relationships without wasting resources.
In this post, we’ll go over how to use G*Power to decide on sample size when studying two continuous variables, like the time students spend on social media and their grades. We’ll also walk through a few example studies to show how researchers set up these calculations and how these are reported in the methodology of the research paper in APA style.
Why is Sample Size Important in Studies that Look for Relationships?
In studies that look for relationships, researchers want to know if two continuous things (like hours of exercise per week and mental health score) are connected. If the sample size is too small, researchers may miss important relationships. On the other hand, if the sample size is too big, it takes longer and costs more money than necessary. Calculating the right sample size helps researchers plan a study that is just the right size to get reliable results.
G*Power and the Bivariate Normal Model Test
G*Power is software that helps researchers calculate sample sizes. It includes many tests for different types of research, including a test for looking at relationships between two continuous variables, which G*Power calls the Bivariate Normal Model. By entering a few details, such as how big you expect the relationship to be and how confident you want to be in your results, G*Power can tell you the number of participants you need.
Important Terms for Calculating Sample Size in Correlation Studies
When setting up G*Power for a study on relationships, you need to understand a few basic terms:
- Effect Size (r): This is an estimate of how strong you think the relationship is between your two variables. It ranges from -1 to 1, where numbers close to 0 mean a weak relationship, and numbers close to -1 or 1 mean a strong relationship. For example, if you expect a weak relationship, you might set the effect size to 0.2; for a moderate relationship, 0.5.
- Alpha Level (α): This is the level of confidence you want in your results. Most researchers use 0.05, which means you have a 5% chance of thinking there’s a relationship when there actually isn’t.
- Power (1 – β): Power is the chance of correctly finding a real relationship. Most studies use a power of 0.80, meaning you want an 80% chance of correctly detecting a relationship if it’s really there.
Example: Using G*Power to Study Social Media and Grades
Suppose a researcher wants to find out if there’s a relationship between time spent on social media and grades for high school students. He expects that more time on social media could be linked to slightly lower grades, with a weak to moderate relationship (around r=−0.25). The effect size of r=−0.25 is negative because it suggests an inverse (or negative) relationship between social media use and grades. In this context, a negative correlation means that as one variable increases, the other tends to decrease.
Here’s how he could set up the power analysis in G*Power:
- Open G*Power (click to download: Windows, Mac) and choose:
- Test Family: Exact
- Statistical Test: Correlation: Bivariate Normal Model
- Type of Power Analysis: A priori (to calculate sample size before collecting data)
- Enter Parameters:
- Tails: Two-tailed (to test for both positive and negative relationships)
- Effect Size r: Enter -0.25
- Alpha (α): 0.05
- Power (1 – β): 0.80
- Correlation ρ Η0: 0 (the null hypothesis often assumes that there is no correlation between the two variables)
- Calculate:
- G*Power will tell him he needs about 123 students.
This means that if the true relationship between social media use and grades is r=−0.25, he’ll need at least 123 participants to have a good chance (80%) of detecting it. This is how he may report the sample size in the methodology part of his research paper (APA style):
“A power analysis was conducted using G*Power (Faul et al., 2007) to determine the required sample size for detecting a correlation between social media use and GPA among high school students. The analysis was based on an expected effect size of r=−0.25, which reflects a small-to-moderate relationship. A two-tailed test was used with an alpha level of .05 and a desired power of .80. Results indicated that a minimum of 123 participants would be necessary to detect a correlation of this magnitude with sufficient statistical power. This sample size ensures an 80% likelihood of correctly identifying a significant relationship if one exists at the specified effect size and alpha level.”
Other Research Examples Using G*Power
Here are a few more example studies that show how researchers might use G*Power to figure out sample size:
Example 1: Physical Activity and Mental Health
A researcher wants to see if there’s a connection between weekly hours of exercise and mental health scores, expecting a moderate positive (or direct) relationship (around r=0.35). In this case, G*Power would suggest he needs about 62 participants for 80% power and an alpha of 0.05. This is how this may be reported in the methodology part of the research paper (APA style):
“A power analysis was conducted to determine the required sample size for detecting a moderate correlation (expected effect size, r = .35) between weekly hours of exercise and mental health scores. Using G*Power (Faul et al., 2007), the analysis indicated that a sample size of 62 participants would be needed to achieve 80% power, with an alpha level of .05.”
Example 2: Income and Life Satisfaction
A sociologist thinks there may be a small positive relationship between income level and life satisfaction (around r=0.20). For this small effect size, G*Power would recommend around 194 participants to get reliable results. This is how this may be reported in the methodology part of the research paper (APA style):
“To examine a hypothesized small positive relationship between income level and life satisfaction (expected effect size, r = .20), a power analysis was conducted. The G*Power software (Faul et al., 2007) determined that a sample of 194 participants would be necessary to reach 80% power, assuming a significance level of .05.”
Example 3: Screen Time and Eye Strain
An eye doctor suspects a moderate link between daily screen time and eye strain severity (around r=0.40). G*Power suggests he needs about 37 participants. This is how this may be reported in the methodology part of the research paper (APA style):
“For investigating the expected moderate correlation (r = .40) between daily screen time and eye strain severity, a power analysis was conducted. According to G*Power (Faul et al., 2007), a sample size of 37 participants would be sufficient to achieve a power of 80%, with an alpha level of .05.”
Each of these studies shows how sample size depends on the expected strength of the relationship. If you expect a smaller effect size, you’ll need a larger sample size to detect it reliably.
Tips for Using G*Power
When using G*Power, it helps to know a few things to make your calculations as accurate as possible. First, try to estimate effect size (how strong you think the relationship is) based on similar research. If you’re just exploring a new question, a lower power level might be okay, like 0.70, but for studies with strong predictions, you might need a higher power, like 0.90. Also, remember to note your alpha level, power, and effect size in your study write-up, so other people understand your sample size choices.
Reference
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191. https://doi.org/10.3758/BF03193146
