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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 mean of a Chi Square distribution is its degrees of freedom. Chi Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom. As the degrees of freedom increases, the Chi Square distribution approaches a normal distribution. Figure 1 shows density functions for three Chi Square distributions.