Understanding Moderated Mediation Power
Moderated mediation asks whether an indirect effect changes across a moderator. A study may look strong in theory, yet still miss the effect when the sample is small. This calculator helps plan that risk before data collection. It uses path estimates, standard errors, moderator values, alpha level, and simulation settings. The goal is not to replace a final statistical package. The goal is to give a transparent planning estimate.
What The Inputs Mean
Path a1 is the effect of X on M when W is zero. Path a3 is the interaction effect between X and W on M. Path b1 is the effect of M on Y when W is zero. Path b3 is the interaction effect between M and W on Y. You may enter zero for a3 or b3 when only one stage is moderated. The standard error fields describe uncertainty at a reference sample size. The tool rescales those errors for the planned sample.
Why Power Matters
Power is the chance of detecting the conditional indirect effect when the assumed model is true. Low power can produce unstable signs, wide intervals, and weak conclusions. Higher power gives a better chance of identifying where mediation is present. It also helps compare several sample designs. Because moderated mediation contains products of paths, small changes in either path can strongly change the indirect effect.
Interpreting The Output
The result table shows the conditional indirect effect at low, mean, and high moderator values. It also shows the delta method standard error, z value, analytic power, and simulation power. The index row summarizes how the indirect effect changes near the selected moderator center. If analytic and simulation power are close, the assumptions are behaving consistently. Large gaps suggest reviewing effect sizes, errors, or sample size.
Planning Advice
Use realistic estimates from prior studies, pilots, or meta-analysis. Avoid entering optimistic effects only to reach a desired sample. Run the calculator several times. Try conservative, expected, and strong effect scenarios. Compare the sample needed for each moderator value. For publication planning, also consider missing data, design effects, nonnormality, measurement error, and planned covariates. Treat this output as a planning guide, then confirm with your chosen analysis workflow and reporting standards.