Understanding Chi-Square Power Analysis
Conducting empirical research requires rigorous methodological planning, particularly when determining the exact participant numbers needed to avoid Type II errors. Statistical power represents the probability that a test correctly rejects a false null hypothesis. For categorical data analyzed via Pearson's chi-square tests, power depends heavily on the chosen effect size, significance threshold, and degrees of freedom.
Formula Used
The core computational engine utilizes Cohen's effect size framework for contingency tables and goodness-of-fit models. The baseline sample size $N$ is derived using normal approximation quantiles for alpha ($Z_\alpha$) and beta ($Z_\beta$):
$$N = \frac{(Z_{\alpha/2} + Z_\beta)^2}{w^2}$$
Where $w$ is Cohen's effect size and the non-centrality parameter $\lambda$ scales directly with total observations and degrees of freedom.
How to Use This Calculator
First, select your specific chi-square test variation from the dropdown menu. Input your anticipated effect size—such as 0.1 for small, 0.3 for medium, or 0.5 for large effects. Specify your alpha level, typically set to 0.05, and your desired statistical power threshold like 0.80. Adjust matrix rows, columns, or contingency dimensions if required. Finally, input expected participant dropout percentages to compute a fully compensated, realistic recruitment sample size.