Before a study, power analysis answers how many subjects you need; after one, it answers what you could have detected. Magic Stat computes both from the same dialog, shows the power curve live as you change the parameters, and documents the formulas against the G*Power conventions.
Power analysis links four quantities: the effect size, the sample size, the significance level and the power (the chance of detecting the effect if it exists). You know three of them and solve for the fourth. Solving for the sample size, given a target power, is the a priori analysis — the one you do when planning a study. Solving for power, given the sample you already collected, is the post hoc analysis. Solving for the smallest effect you could detect, given the sample and a target power, is the sensitivity analysis.
The honesty caveat belongs here. Post hoc power computed from the effect size you observed is a monotone function of the p-value; a non-significant result will look "underpowered" by construction. It is a weak argument for the value of a study that has already been run, and reporting it as if it rescued a null result is a known misuse. The a priori analysis, done before data collection and with an effect size justified from the literature or from a pilot, is where power analysis earns its place.
The tests covered run from the common ones — independent and paired t-tests, one-way ANOVA, correlation, chi-square, multiple regression — to repeated-measures ANOVA and structural equation models with RMSEA-based fit tests. Effect sizes can be typed in directly or computed from descriptive statistics with a calculator in the same style as G*Power's "Determine".
Analysis types: A priori — required sample size · Post hoc — achieved power · Sensitivity — required effect size.
Parameters: alpha · target power · n · ratio n2/n1 · groups (k) · chi-square df · predictors (p) · measures (nm) · nonsphericity ε · model df · H0 RMSEA · true RMSEA.
Effect-size calculator: Cohen's d, d_z, f, f², w, h or r from means and standard deviations, proportions or R².
Output: the solved quantity stated in words, plus a live power-versus-n curve rendered as a figure.
The a priori analysis: you state the test, an effect size justified from the literature or a pilot, the alpha and the target power, and the app returns the sample size. That is the analysis a reviewer expects to see before data collection, not after.
Rarely. Power computed from the effect you observed in the same sample is a transformation of the p-value: a non-significant result will always look underpowered, and a significant one will always look adequately powered. It is not a good defence of a study that has already been run, and the app does not present it as one.
The formulas are documented against the G*Power and WebPower conventions and the repeated-measures case follows the Potvin and Schutz approach. For an unusual design, cross-checking a single number against G*Power is still a sensible habit — agreement is the point of documenting the conventions.
Then power depends on the design, not only on the effect size and n: the number of clusters and their size both matter, and a simple formula will mislead. For those designs, a simulation or a design-specific tool is the honest route; the app's power analysis targets the single-level tests listed in the dialog.
No — power analysis runs locally from the values you type, and the only automatic signal is an anonymous installation counter.