Effect Sizes

What It Is

In MCPower, effect sizes are standardized regression coefficients (betas). A beta of 0.30 means that a one standard deviation increase in the predictor is associated with a 0.30 standard deviation change in the outcome. This standardization makes effects comparable across variables measured on different scales.

For binary and factor predictors, the interpretation shifts slightly. A binary effect of 0.50 means that switching from the reference group (0) to the treatment group (1) produces a 0.50 SD change in the outcome. For factors, each dummy variable gets its own effect size representing the difference between that level and the reference level.

Effect sizes are the single most important input to a power analysis. Overestimating them leads to underpowered studies; underestimating them wastes resources. The best source is prior research or pilot data. When neither is available, Cohen’s (1988) benchmarks provide a starting point.

How It Works in MCPower

Set effect sizes with set_effects():

model.set_effects("treatment=0.50, age=0.25, group[2]=0.40, group[3]=0.60")

For factor variables, each non-reference level needs its own effect size using bracket notation (e.g., group[2]=0.40).

set_effects() must be called before running the analysis. Any predictors not explicitly assigned an effect size default to 0.0 (no effect).

Guidelines

Cohen’s Benchmarks

Predictor Type

Small

Medium

Large

Continuous

0.10

0.25

0.40

Binary / Factor

0.20

0.50

0.80

Why Different Benchmarks for Binary vs Continuous?

For binary/factor predictors, MCPower keeps binary variables as 0/1 (not standardized), so the beta coefficient equals Cohen’s d directly. The benchmarks (0.20/0.50/0.80) are Cohen’s (1988) standard conventions.

For continuous predictors, variables are standardized to N(0,1), so beta represents the change in Y per 1-SD change in X. These benchmarks are calibrated so that a continuous predictor at the “medium” threshold (beta = 0.25) produces approximately the same statistical power as a binary predictor at Cohen’s medium effect (d = 0.50), holding sample size constant. This power-equivalence approach ensures the labels “small,” “medium,” and “large” carry consistent practical meaning across predictor types.

Practical Interpretation

Beta

What It Looks Like

0.10

Barely noticeable in raw data. Requires large samples to detect.

0.20

Small but real effect. Visible with careful measurement.

0.30

Moderate. A trained observer would notice the pattern.

0.50

Clearly visible. Obvious group differences in plots.

0.80+

Dramatic. Hard to miss even in small samples.

Interactions

Interaction effects (e.g., x1:x2) are typically smaller than main effects. Values of 0.10–0.20 are common. Plan for lower power when testing interactions.

Factor Variables

Each dummy variable gets its own beta relative to the reference level. If two non-reference levels have different betas (e.g., 0.30 and 0.70), the implicit contrast between them is the difference (0.40). This matters for post-hoc comparisons.

Common Patterns

Typical Effect Sizes by Field

Field

Predictor

Typical Beta

Notes

Education

Teaching intervention

0.20–0.40

Medium effects common

Education

Socioeconomic status

0.15–0.30

Small-medium

Psychology

Therapy vs. control

0.30–0.60

Medium-large

Psychology

Personality trait

0.10–0.25

Small-medium

Medicine

Drug vs. placebo

0.20–0.50

Varies widely

Medicine

Lifestyle factor

0.05–0.20

Often small

Social science

Policy intervention

0.10–0.30

Small-medium

Marketing

Ad exposure

0.05–0.15

Typically small

Rules of Thumb

  • When in doubt, use a smaller effect size. Overestimation is the more costly error.

  • Use Scenario Analysis to test sensitivity to effect size uncertainty.

  • If prior literature reports Cohen’s d, it maps roughly to beta for a binary predictor.

  • Main effects are almost always larger than interaction effects in the same model.

Learn More

References

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.