# Chi-square

### Chi-square (χ²) Test of Independence

May 22, 2017

BRIEF DESCRIPTION Whereas the One-sample Chi-square (χ²) goodness-of-fit test compares our sample distribution (observed frequencies) of a single variable with a known pre-defined distribution (expected frequencies) such as the population distribution, normal distribution, or poisson distribution, to test for the significance of deviation, the Chi-square (χ²) Test of Independence compares two categorical variables in a cross-tabulation fashion to determine group differences or degree of association (or non-association i.e. independence).  Chi-square (χ²) is a [READ MORE]

### Outlier cases – bivariate and multivariate outliers

August 14, 2016

In follow-up to the post about univariate outliers, there are a few ways we can identify the extent of bivariate and multivariate outliers:   First, do the univariate outlier checks and with those findings in mind (and with no immediate remedial action), follow some, or all of these bivariate or multivariate outlier identifications depending on the type of analysis you are planning.  _____________________________________________________ BIVARIATE OUTLIERS: For one-way ANOVA, we can use the GLM (univariate) procedure to save standardised or studentized residuals. Then do a normal [READ MORE]

### 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]

### Which Test: Chi-Square, Logistic Regression, or Log-linear analysis

November 19, 2013

In a previous post I have discussed the differences between logistic regression and discriminant function analysis, but how about log-linear analysis? Which, and when, to choose between chi-square, logistic regression, and log-linear analysis?   Lets briefly review each of these statistical procedures: The chi-square test (χ²) is a descriptive statistic, just as correlation is descriptive of the association between two variables. Chi-square is not a modeling technique, so in the absence of a dependent (outcome) variable, there is no prediction of either a value (such as in ordinary [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]

### Which test: Compare a single group mean or frequency to a hypothetical / known value or proportion

July 16, 2012

When the research objective is to compare a single group mean or frequency to a hypothetical / known value or proportion (such as an action standard or a norm), we have a choice among different statistical procedures, depending on the following variable characteristics:   Number of variables:  One dependent variable   Examples:  Is our mean customer satisfaction score significantly different from the industry average (or action standard) of e.g. 4.6? Is the 54/46 gender proportion in our sample significantly different from the population’s age proportions of 51/49?  When [READ MORE]