When planning a study to check if a sample’s average significantly differs from a known reference value, it’s essential to choose the right sample size. With a sample size that’s too small, there’s a risk of missing a significant difference (underpowered study). A sample that’s too large, however, can lead to wasted time and resources. Using G*Power software, researchers can calculate the ideal sample size to reliably detect meaningful differences.
This guide will demonstrate how to use G*Power to determine the necessary sample size for a one-sample t-test, where we compare the mean of a sample against a constant value. We’ll also look at example research scenarios, walk through the G*Power setup, and provide an example of how this sample size determination would be reported in an academic paper using APA style.
Why Sample Size is Important in One-Sample T-Tests
In one-sample t-tests, researchers test whether the average of a sample significantly differs from a specific reference value. A one-sample t-test is appropriate in scenarios where you already know the reference value you want to compare against. For example, testing if high school students’ average sleep time is significantly different from the recommended 8 hours of sleep per night. An adequately calculated sample size ensures that if a real difference exists, the study is likely to detect it, while avoiding unnecessary data collection.
Using G*Power for One-Sample T-Test Power Analysis
G*Power software is widely used for power analysis across various research designs (click to download: Windows, Mac). For a one-sample t-test, we use G*Power’s T tests family and select the Means: Difference from constant (one sample case) as the statistical test. The parameters we enter into G*Power depend on three key terms: effect size, alpha level, and power.
- Effect Size (Cohen’s d): This indicates the expected strength of the difference between the sample mean and the constant. A small effect size (d = 0.2) suggests a slight difference, while a larger effect size (d = 0.5 or d = 0.8) suggests a moderate or large difference, respectively.
- Alpha Level (α): This represents the probability of a false positive, typically set at 0.05, which means a 5% risk of concluding there’s a difference when there isn’t one.
- Power (1 – β): The probability of correctly detecting a difference if one exists. Researchers commonly use 0.80, indicating an 80% chance of detecting a true difference.
Example 1: Analyzing Sleep Patterns in High School Students
Imagine a researcher wants to determine whether high school students in a particular school sleep significantly less than the recommended 8 hours per night. This question requires a one-sample t-test because the researcher is comparing the average sleep of the sample to a constant (8 hours).
- Effect Size (d): The researcher expects a small effect size of 0.3, indicating a minor but potentially meaningful difference from 8 hours.
- Alpha Level: 0.05 (5% chance of a false positive).
- Power: 0.80 (80% likelihood of detecting a true difference).
Steps in G*Power
To set up this power analysis in G*Power:
- Open G*Power and select:
- Test Family: T tests
- Statistical Test: Means: Difference from constant (one sample case)
- Type of Power Analysis: A priori (for determining sample size before data collection)
- Enter the following parameters:
- Effect Size d: 0.3
- Alpha (α): 0.05
- Power (1 – β): 0.80
- Click Calculate.
After entering these values, G*Power shows that the required sample size is approximately 88 students. This sample size will give the researcher an 80% chance of detecting a difference from 8 hours of sleep if one truly exists.
Sample Size Reporting in APA Style
Here is how the sample size determination might be reported in the methodology section of a research paper:
“A power analysis was conducted using G*Power (Faul et al., 2007) to determine the necessary sample size for detecting a difference in average sleep duration from the recommended 8 hours per night. Based on a small expected effect size (d = 0.3), an alpha level of .05, and a desired power of .80, the analysis indicated that a minimum sample size of 88 students would be required. This sample size ensures an 80% probability of detecting a significant difference from the reference sleep duration if one exists, while controlling for the risk of a Type I error at 5%.”
Example 2: Testing Exam Scores Against a National Standard
A teacher wants to see if her class’s average math test score differs from the national average score of 75. She expects a moderate difference and sets an effect size of 0.5. G*Power would calculate a sample size of approximately 34 students to achieve sufficient power with an alpha of 0.05 and power of 0.80. This result could be reported as follows:
“A power analysis was conducted to determine the required sample size for a one-sample t-test comparing the mean math score of the class to the national average (M = 75). Using G*Power (Faul et al., 2007) with an expected moderate effect size (d = 0.5), an alpha level of .05, and a desired power of .80, the analysis recommended a sample size of 34 students. This sample size provides an 80% likelihood of detecting a significant difference from the national average if one is present.”
Example 3: Testing Average Screen Time Against Recommended Levels
A researcher wants to know if a group of college students spends more screen time on their phones than the recommended maximum of 2 hours per day, which is suggested to reduce eye strain and maintain good mental health. This study will use a one-sample t-test because the researcher is comparing the sample mean (average screen time of students) to the known constant of 2 hours. She anticipates a moderate effect size (d = 0.5), meaning she expects students may significantly exceed the recommendation. To calculate the needed sample size, the researcher sets an alpha level of 0.05 (indicating a 5% risk of wrongly concluding there’s a difference) and a power of 0.80 (indicating an 80% chance of finding a difference if one exists).
In reporting this for a research paper, the following APA style might be used:
“A power analysis was conducted using G*Power (Faul et al., 2007) to determine the sample size necessary to detect a difference in average daily screen time from the recommended maximum of 2 hours per day. Assuming a moderate effect size (d = 0.5), an alpha level of .05, and a desired power of .80, the analysis indicated that a sample size of 34 participants would be sufficient. This sample size allows an 80% probability of detecting a difference if students’ screen time differs from the recommendation.”
Example 4: Testing College GWA Against National Average
A college dean is curious if the average GWA of students at her institution is different from the national average of 1.75. The dean uses a one-sample t-test, comparing her college’s average GPA to this benchmark. Expecting only a small difference (d = 0.2) since her college has similar academic standards to others, she sets an alpha level of 0.05 and a power of 0.80.
In her research report, she might include the following APA-style write-up:
“To determine the necessary sample size for comparing the college’s average GPA to the national average of 3.0, a power analysis was conducted using G*Power (Faul et al., 2007). The analysis was based on a small expected effect size (d = 0.2), an alpha level of .05, and a desired power of .80. Results indicated that a sample size of 199 students would be required to detect a difference from the national average GPA with adequate power. This sample size ensures an 80% probability of identifying a significant difference if one exists, even if the effect is small.”
Key Takeaways
These examples show how sample size calculations depend on the expected effect size and the study’s design. For smaller expected effects, a larger sample is required to detect differences reliably. Using G*Power, researchers can efficiently determine the optimal sample size to achieve their study’s goals without unnecessary data collection.
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
