Goodness-of-fit test

One-Sample Chi-square (χ²) goodness-of-fit test

January 9, 2016

BRIEF DESCRIPTION The Chi-square (χ²) goodness-of-fit test is a univariate measure for categorical scaled data, such as dichotomous, nominal, or ordinal data.  It tests whether the variable’s observed frequencies differ significantly from a set of expected frequencies. For example, is our observed sample’s age distribution of 20%, 40%, 40% significantly different from what we expect (e.g. the population age distribution) of 30%, 30%, 40%. Chi-square (χ²) is a non-parametric procedure.   SIMILAR STATISTICAL PROCEDURES: Binomial goodness-of-fit (for binary data) [READ MORE]

One-Sample Kolmogorov-Smirnov goodness-of-fit test

February 8, 2015

BRIEF DESCRIPTION The Kolmogorov-Smirnov (K-S) test is a goodness-of-fit measure for continuous scaled data. It tests whether the observations could reasonably have come from the specified distribution, such as the normal distribution (or poisson, uniform, or exponential distribution, etc.), so it most frequently is used to test for the assumption of univariate normality. The categorical data counterpart is the Chi-Square (χ²) goodness-of-fit test. The K-S test is a non-parametric procedure.     SIMILAR STATISTICAL PROCEDURES: Adjusted Kolmogorov-Smirnov Lilliefors test (null [READ MORE]

Which test: Compare a single group distribution to a hypothetical / known distribution (goodness-of-fit tests)

July 16, 2012

When the research objective is to compare a single group distribution to a hypothetical / known distribution (goodness-of-fit tests), we have a choice among different statistical procedures, depending on the following variable characteristics:   Number of variables:  One dependent variable   Examples:  Does our sample data distribution fit the binomial / normal / poisson curve? Is our interval-measured sample distribution significantly different from a normal distribution (goodness-of-fit for normality)? Is the 10%/20%/20%/30%/20% age proportions in our sample significantly [READ MORE]