Describing Associations

Chi-square (χ²) Test of Independence

April 22, 2023

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]

Which test: Quantify the association / relationship / correlation / dependence between two variables

October 12, 2020

When the research objective is to understand the association / relationship / correlation / dependence between two variables, we have a choice among different statistical procedures, depending on the following variable characteristics: Number of variables: One dependent variable and one independent variable (technically we don’t distinguish between a dependent and independent variable in these procedures). Examples: To what extent are two variables related to each other? Is one variable dependent on another variable? When the variables are BINOMIAL / BINARY / [READ MORE]

Correlation and covariance matrices

July 30, 2020

Many statistical procedures such as the ANOVA family, covariates and multivariate tests rely on either covariance and/or correlation matrices. Statistical assumptions, such as Levene’s test for homogeneity of variance, the Box’s M test for homogeneity of variance-covariance matrices, and the assumption of sphericity specifically address the properties of the variance-covariance matrix (also referred to as the covariance matrix, or dispersion matrix). The covariance matrix as shown below indicates the variance of the scores on the diagonal and the covariance on the [READ MORE]

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

August 19, 2019

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 / procedures? How do we decide?

July 2, 2017

With so many statistical procedures available, how do we decide which tests are best to address our research objectives? (several posts deal with this topic). First and foremost, the decision as to which statistical procedures to apply to the data should be made BEFORE the design of the data collection instrument (e.g. the questionnaire), and not AFTER data has been collected. Plan ahead so that your analysis are entirely focused on addressing your research objectives and NOT to address your data. Too many researchers remain guilty of waiting to see the data so they can decide what to [READ MORE]