Introducing G*Power for Sample Size Calculation for Structural Equation Modeling
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Use G*Power’s F-test route: Test family = F tests and Statistical test = Linear multiple regression: Fixed model, R square deviation from zero.
Briefing
G*Power can be used to estimate the minimum sample size needed for structural equation modeling (SEM) by running an F-test for a fixed linear multiple regression model based on R² deviation from zero. The practical workflow starts with selecting the correct test family and statistical test settings, then entering an assumed effect size, a target statistical power, and the number of predictors. For researchers planning data collection, this turns “how many participants do I need?” into a concrete number before any data exist.
In the transcript’s first example, the setup assumes three predictors influencing a single outcome and uses the “F test” path in G*Power: Test family → F tests, then Statistical test → Linear multiple regression: Fixed model, R² deviation from zero. The key input is effect size f² (expressed through common benchmarks): 0.02 for small, 0.15 for medium, and 0.35 for large. While there’s no universal “ideal” effect size, the guidance is to typically start with a medium effect (0.15) in the absence of strong prior evidence, or alternatively derive f² from what similar studies report in the relevant field.
Power is set to a default of 0.95 in the example, with a minimum commonly accepted threshold of 0.80 in applied research. With three predictors and the medium-effect assumption, the calculation yields a minimum required sample size of 77. The transcript emphasizes that this is a planning number: it supports deciding whether a study is likely to detect the hypothesized relationships with the chosen power.
A second example addresses moderation, where additional predictors emerge from interaction terms. When a model includes a moderator, the analysis introduces an interaction term, increasing the effective predictor count. With one predictor plus a moderator (and thus an interaction), the transcript treats the model as having three predictors total. Extending the idea further, two moderators (M1 and M2) create two interaction terms, raising the predictor count to five.
Using the same minimum power of 0.80 and the expanded predictor set, the required sample size becomes 92. The transcript then shows how stronger effects reduce sample size needs: increasing the effect size lowers the minimum required sample size to 43. Overall, the message is straightforward—G*Power’s SEM-oriented sample size planning hinges on selecting the right F-test model, choosing an effect size grounded in theory or prior literature, and accounting for how moderation increases the number of predictors through interaction terms.
Cornell Notes
G*Power can estimate minimum sample sizes for SEM-related regression models using an F-test for “Linear multiple regression: Fixed model, R² deviation from zero.” The process requires choosing an effect size f² (0.02 small, 0.15 medium, 0.35 large), setting statistical power (often 0.80 minimum; 0.95 used as a default in one example), and specifying the number of predictors. With three predictors and a medium effect size, the minimum sample size is 77. Moderation increases the number of predictors because interaction terms are added during analysis; with two moderators (and two interaction terms), the predictor count rises to five and the minimum sample size becomes 92 at 0.80 power. If the effect size is larger, the required sample size drops substantially (down to 43 in the example).
How does a researcher select the correct G*Power settings for sample size planning in this workflow?
What effect size inputs are used, and how should an effect size be chosen when no prior data exist?
What role does statistical power play, and what thresholds are mentioned?
Why does adding moderators increase the number of predictors in the sample size calculation?
How do the transcript’s sample size results change across predictor count and effect size?
Review Questions
- In G*Power, which specific test family and statistical test options are used for the R² deviation from zero approach?
- How do moderation and interaction terms change the effective number of predictors for sample size planning?
- What happens to the required sample size when you increase the assumed effect size in the transcript’s examples?
Key Points
- 1
Use G*Power’s F-test route: Test family = F tests and Statistical test = Linear multiple regression: Fixed model, R square deviation from zero.
- 2
Choose an f² effect size using benchmarks (0.02 small, 0.15 medium, 0.35 large) or derive it from prior studies in the same research area.
- 3
Set statistical power deliberately; 0.80 is treated as a common minimum, while 0.95 appears as a default in the example.
- 4
Count predictors carefully for moderation models because interaction terms add predictors during analysis.
- 5
In the transcript’s baseline case (three predictors, medium effect), the minimum sample size is 77.
- 6
In the moderation case with two moderators (five effective predictors) at 0.80 power, the minimum sample size is 92.
- 7
Assuming larger effects reduces required sample size; the example drops to 43 when effect size increases.