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What is Chi-square? History and Definition . A chi-square distribution is the distribution of the sum of squares of k independent standard normal random variables with k degree of freedom. A chi-square test is a statistical hypothesis test where the null hypothesis that the distribution of the test statistic is a chi-square distribution, is true. While the chi-square distribution was first introduced by German statistician Friedrich Robert Helmert, the chi-square test was first used by Karl Pearson in 1900.
The test statistic follows, approximately, a chi-square distribution with (k-c) degrees of freedom where k is the number of non-empty cells and c = the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution + 1.or example, for a 3-parameter Weibull distribution, c = 4. where \(\chi^2_{1-\alpha, \, k-c}\) is the chi-square critical value with k-c degrees of freedom and significance level Î±.