Chi-Square Goodness-of-Fit
Chi-square = sum((observed - expected)^2 / expected) on k-1 df, the p-value from the chi-square CDF, and a reject / fail-to-reject verdict at alpha. Expected entered as counts or proportions; flags expected counts below 5. Per OpenIntro Statistics Ch. 6.
Formula and source
Chi-square statistic = sum((observed - expected)^2 / expected) over k categories, on k - 1 degrees of freedom. p-value = 1 - chi2Cdf(chi-square, k - 1). Expected proportions are scaled to the observed total. Reject H0 (the observed counts follow the expected distribution) when p < alpha.
OpenIntro Statistics 4th ed. Chapter 6 (inference for categorical data) by name; the chi-square CDF via the regularized lower incomplete gamma function per Numerical Recipes in C 2nd ed. ยง6.2.
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