Chisquared test for goodness of fit also written as a χ2 test is any statistical hypothesis test wherein the sampling distribution of the test statistic is a chisquared distribution when the null hypothesis is true. Without other qualification, ‘chisquared test’ often is used as short for Pearson’s chisquared test. Chisquared tests are often constructed from a sum of squared errors, or through the sample variance. Test statistics that follow a chisquared distribution arise from an assumption of independent normally distributed data, which is valid in many cases due to the central limit theorem. A chisquared test can be used to attempt rejection of the null hypothesis that the data are independent. Also considered a chisquared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chisquared distribution as closely as desired by making the sample size large enough. The chisquared test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.
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