6.3. Goodness of Fit Tests
The Goodness of Fit Tests are used to determine whether two samples have similar distributions. The main difference between chi-square tests and Kolmogorov-Smirnov Tests is that the former are used with frequency data while the latter with continuous data.
If you want to test whether a sample is normally distributed (when the population mean and standard deviation are not known and are to be estimated from the data), you can use the Normality Tests procedure. The four tests supported are Shapiro-Wilk, Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling.
The Chi-Square Tests expect data in the form of frequency counts. In Stand-Alone Mode, raw data can easily be transformed into the frequency counts format using the Data Processor’s Freq() function (see 188.8.131.52. Statistical Functions).
In case of one sample tests, the second sample is assumed to have a known distribution function such as uniform or normal. In two sample tests the second sample may be just another set of observed data, in which case the test will only determine whether the two samples have similar distributions, or it may contain expected values from a theoretical distribution function, in which case the test will determine whether the first sample has a distribution consistent with a particular theoretical distribution function.