Chi-Square Test of Independence Calculator

A chi-square test of independence checks whether two categorical variables are related or whether any pattern in a table could just be chance. This calculator handles the common 2x2 case, where you have two rows and two columns of counts, such as treatment versus no treatment crossed with success versus failure. You enter the four observed counts, labelled a, b, c and d, and the tool works out the expected count for each cell from the row and column totals, then sums the squared differences between observed and expected, each divided by its expected value. The result is the chi-square statistic together with its degrees of freedom, which is always one for a 2x2 table. Researchers, students, marketers, and health and social science analysts in New Zealand use this to test associations, for example whether a campaign changed conversion or whether an outcome depends on a group. To read the result, compare the chi-square value with a critical value from a chi-square table at your chosen significance level, commonly 3.84 for one degree of freedom at the 5 percent level; a larger statistic suggests the variables are not independent. For the test to be reliable, use raw counts rather than percentages, make sure each expected count is at least five, and consider Yates continuity correction or Fisher's exact test when counts are small. Remember that the test shows association, not cause, so a significant result tells you the variables move together but not why. Always report the sample size alongside the statistic so others can judge the strength and reliability of your finding before drawing conclusions.

Expected = row total * column total / grand total. Chi-square = sum of (observed - expected)^2 / expected, df = 1.