Run a chi-square goodness-of-fit test comparing observed vs expected frequencies.
The chi-square goodness-of-fit test measures how well observed categorical data match an expected distribution. Large χ² values (small p-values) indicate the observed data differ significantly from what was expected.
χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ
Observations must be independent, all expected frequencies should be at least 5, and the data must be counts (not proportions or means).
A p-value below your significance level (commonly 0.05) means you reject the hypothesis that the data follow the expected distribution.