Goodness of Fit Tests for Identifying Nonnormal Data

Abstract

Goodness of fit for assessing normal distribution of a data file is an important requirement for normal and t-distributed tests to be sensitive for statistical testing the data. Data files that lack goodness of fit can be analyzed using distribution free methods, like Monte Carlo modeling and neural network modeling (SPSS for Starters, Part 2 from the same authors, Chaps. 18 and 19, Springer New York, 2012, from the same authors). The chi-square and the Kolmogorov-Smirnov goodness of fit tests are pretty much similar, but one uses the differences between all observed and expected observations, while the other uses the single largest difference between observed and expected observations, and, so, results may not be identical. One test may, however, very well be used as a complementary test or contrast test to the other.