About the Chi-Square Test
The chi-square (χ²) test compares observed counts with the counts you would expect. The goodness-of-fit test asks whether one set of counts follows a given distribution (is a die fair? are sales equal across days?). The test of independence asks whether two categorical variables in a table are related (is preference linked to gender?).
Enter counts — one row for goodness of fit (with expected counts or proportions, or leave them equal), or a table with rows separated by semicolons for independence. The calculator shows each cell’s contribution, χ², degrees of freedom, the p-value, the critical value and a plain decision, and warns if expected counts are below 5.