When conducting research, it is important to have enough participants to detect meaningful differences between groups. If the sample size is too small, there is a high chance of missing real effects. If the sample size is too large, unnecessary resources are used and the study might detect trivial effects that are not practically meaningful. This is where G*Power, a free statistical software, helps researchers determine the right number of participants for their study.
When to Use G*Power for One-Way ANOVA
The one-way ANOVA (fixed effects, omnibus) in G*Power is used when:
- You want to compare the means of three or more independent groups.
- The independent variable is categorical (nominal/ordinal), with fixed levels (i.e., not randomly sampled).
- The dependent variable is continuous (interval/ratio).
- The test assumes homogeneity of variance across groups (Levene’s Test should be checked).
- The design does not include repeated measures (each subject belongs to only one group).
Understanding Power Analysis in ANOVA
Power analysis helps determine the minimum sample size required to detect a statistically significant effect. The key components of power analysis include the effect size, significance level, statistical power, and number of groups.
Effect size (f) measures the strength of differences among group means. Cohen (1988) established benchmarks for interpretation: small (f = 0.10), medium (f = 0.25), and large (f = 0.40). In most research scenarios, a medium effect size is used unless prior studies suggest otherwise. The significance level (α) represents the probability of a Type I error, with a standard value of 0.05 (5%). Statistical power (1-β) indicates the probability of detecting a true effect, commonly set at 0.80 (80%). The number of groups represents the levels of the independent variable. For instance, a study comparing lecture-based, flipped classroom, and blended learning methods would have three groups.
Research Scenario: The Effect of Teaching Methods on Student Performance
A researcher seeks to determine whether different teaching methods lead to significant differences in student performance in college algebra. The study includes three instructional approaches: lecture-based, flipped classroom, and blended learning. The independent variable is teaching method, while the dependent variable is final exam score (measured on a 0–100 scale).
In this study:
- Outcome Variable: Final exam score (0–100 scale)
- Predictor Factor: Teaching method (lecture-based, flipped classroom, or blended learning)
Step-by-Step Input in G*Power: Open your G*Power. It is free and downloadable online (click to download: Windows, Mac). Use the following inputs:
- Test family: F-tests
- Statistical test: ANOVA: Fixed effects, omnibus, one-way
- Type of Power Analysis: A priori (compute required sample size given α, power, and effect size)
Input parameters
To determine the required sample size, G*Power is used to perform a power analysis with the following settings:
- Effect Size: A medium effect size (f = 0.25), which aligns with prior research on instructional methods.
- Significance Level (Alpha): Set at 0.05, meaning a 5% chance of Type I error.
- Power: Set at 0.80 (80%), ensuring a high probability of detecting a real effect.
- Number of Groups: Three (one for each teaching method).
The G*Power results indicate that 159 participants are required, with 53 participants per group. To account for potential dropouts, an additional 10% is added, bringing the final sample size to 177 participants.
Reporting in APA Style:
“A power analysis using GPower 3.1 (Faul et al., 2007) was conducted to determine the appropriate sample size for a one-way ANOVA. Using a medium effect size (f = 0.25), a significance level of α = .05, and a power of 0.80, the analysis indicated that 159 participants were required, with 53 per group. To account for potential attrition, the final sample size was increased to 177 participants.”
Adjustments for Real-World Research
If dropout rates are expected, researchers should increase the sample size accordingly. A 10% dropout rate requires recruiting 177 participants, while a 15% dropout rate requires 187 participants. If a smaller effect size is expected (f = 0.10), G*Power suggests a much larger sample, approximately 1,179 participants, highlighting the importance of pilot studies and meta-analyses to estimate realistic effect sizes.
Scenario 2
Comparing Weight Loss Across Different Diet Types
A researcher is interested in determining whether different diet types lead to significant differences in weight loss. The study includes four diet plans: low-carb, low-fat, Mediterranean, and vegan. The independent variable is the type of diet, while the dependent variable is weight loss (measured in kilograms).
In this study:
- Outcome Variable: Weight loss (measured in kilograms)
- Predictor Factor: Diet type (low-carb, low-fat, Mediterranean, or vegan)
To determine the required sample size, G*Power is used to perform a power analysis with the following settings:
- Effect Size: A medium effect size (f = 0.30), which aligns with prior studies on dietary interventions.
- Significance Level (Alpha): Set at 0.05, meaning a 5% chance of Type I error.
- Power: Set at 0.80 (80%), ensuring a high probability of detecting a real effect.
- Number of Groups: Four (one for each diet type).
The G*Power results indicate that 128 participants are required, with 32 participants per group. To account for potential dropouts, an additional 10% is added, bringing the final sample size to 140 participants.
Reporting in APA Style:
“A power analysis was conducted using GPower 3.1 (Faul et al., 2007) to determine the necessary sample size for a one-way ANOVA with four independent groups. Using an effect size of f = 0.30, a significance level of α = .05, and a power of 0.80, the analysis indicated a required sample size of 128 participants (32 per group). To adjust for possible attrition, the sample size was increased to 140 participants.”
Scenario 3
Comparing VO2 Max Improvements Across Exercise Types
This study investigates whether different exercise types result in significant differences in VO2 max improvement, a measure of cardiovascular fitness. Participants are assigned to one of three exercise regimens: high-intensity interval training (HIIT), endurance running, or resistance training. The independent variable is the exercise type, while the dependent variable is VO2 max improvement (measured in mL/kg/min).
In this study:
- Outcome Variable: VO2 max improvement (measured in mL/kg/min)
- Predictor Factor: Exercise type (HIIT, endurance running, or resistance training)
To determine the appropriate sample size, G*Power is used with the following parameters:
- Effect Size: A medium effect size (f = 0.20) based on prior studies in exercise science.
- Significance Level (Alpha): Set at 0.05 to minimize the risk of Type I error.
- Power: Set at 0.80, ensuring an 80% likelihood of detecting a significant effect.
- Number of Groups: Three (one for each exercise type).
G*Power results indicate that 199 participants are necessary, with 67 participants per group. To account for possible dropouts, the final sample size is increased to 220 participants.
Reporting in APA Style:
“A power analysis was conducted using GPower 3.1 (Faul et al., 2007) to determine the appropriate sample size for a one-way ANOVA with three independent groups. Using an effect size of f = 0.20, a significance level of α = .05, and a power of 0.80, the analysis suggested a minimum of 199 participants (67 per group). To adjust for potential attrition, the sample size was increased to 220 participants.”
Scenario 4
Comparing Sleep Quality Across Different Bedtime Routines
A researcher investigates whether different bedtime routines lead to significant differences in sleep quality. The study examines three routines: reading before bed, listening to calming music, and using a smartphone. The independent variable is bedtime routine, while the dependent variable is sleep quality score (measured using a validated sleep questionnaire).
In this study:
- Outcome Variable: Sleep quality score (measured using a validated sleep questionnaire)
- Predictor Factor: Bedtime routine (reading, listening to music, or using a smartphone)
To determine the required sample size, G*Power is used to perform a power analysis with the following settings:
- Effect Size: A medium effect size (f = 0.25), consistent with prior sleep studies.
- Significance Level (Alpha): Set at 0.05, meaning a 5% chance of Type I error.
- Power: Set at 0.80 (80%), ensuring a high probability of detecting a real effect.
- Number of Groups: Three (one for each bedtime routine).
The G*Power results indicate that 159 participants are required, with 53 participants per group. To account for potential dropouts, an additional 10% is added, bringing the final sample size to 177 participants.
Reporting in APA Style:
A power analysis was conducted using GPower 3.1 (Faul et al., 2007) to determine the necessary sample size for a one-way ANOVA with three independent groups. Using an effect size of f = 0.25, a significance level of α = .05, and a power of 0.80, the analysis indicated a required sample size of 159 participants (53 per group). To adjust for possible attrition, the sample size was increased to 177 participants.
Scenario 5
Comparing Stress Levels Across Different Work Schedules
A researcher aims to examine whether work schedules lead to significant differences in stress levels among employees. The study includes three types of work schedules: fixed shifts, rotating shifts, and flexible schedules. The independent variable is work schedule, while the dependent variable is stress level (measured using a standardized stress scale).
In this study:
- Outcome Variable: Stress level (measured using a standardized stress scale)
- Predictor Factor: Work schedule (fixed shifts, rotating shifts, or flexible schedules)
To determine the required sample size, G*Power is used to perform a power analysis with the following settings:
- Effect Size: A medium effect size (f = 0.25), based on prior workplace stress studies.
- Significance Level (Alpha): Set at 0.05, meaning a 5% chance of Type I error.
- Power: Set at 0.80 (80%), ensuring a high probability of detecting a real effect.
- Number of Groups: Three (one for each work schedule).
The G*Power results indicate that 159 participants are required, with 53 participants per group. To account for potential dropouts, an additional 10% is added, bringing the final sample size to 177 participants.
Reporting in APA Style:
“A power analysis was conducted using GPower 3.1 (Faul et al., 2007) to determine the necessary sample size for a one-way ANOVA with three independent groups. Using an effect size of f = 0.25, a significance level of α = .05, and a power of 0.80, the analysis indicated a required sample size of 159 participants (53 per group). To adjust for possible attrition, the sample size was increased to 177 participants.”
For a medium effect size, a sample of 159 participants (53 per group) provides 80% power. To account for attrition, at least 177 participants should be recruited. If expecting a small effect, a much larger sample is required, often exceeding 1,000 participants. Researchers must check ANOVA assumptions, including normality and homogeneity of variances, before proceeding with analysis. If the ANOVA results are significant, post-hoc comparisons, such as Tukey’s HSD, should be conducted.
Conducting a power analysis using G*Power should be an essential step in study planning to ensure that research findings are reliable and meaningful.
Reference
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
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
