Basic Concepts In the non-comprehensive models at least one of the variables is not used. We show how to calculate the expected frequencies for one such model, namely (A, B). The degrees of freedom are abc – (a – 1) – (b – 1) –1 = abc – a – b + 1. Example Figure … Read More
Basic Concepts The homogeneous association model for (AB, BC, AC) consists of the saturated model with the λABC term dropped. It therefore has (a – 1)(b – 1)(c – 1) degrees of freedom. For Example 1 of Three-way Contingency Tables this is (2 – 1)(2 – 1)(3 – 1) = 2 degrees of freedom. For … Read More
Basic Concepts The model for (A, B, C) is ln y = λ + λA + λB + λC and has abc – [(a – 1) + (b – 1) + (c – 1) + 1] = abc – (a+b+c) + 2 degrees of freedom. For Example 1 of Three-way Contingency Tables the mutual independence … Read More
Basic Concepts There are three partial independence models (A, BC), (B, AC) and (C, AB). We’ll look at the first of these; the others are similar. The model for (A, BC) consists of the saturated model with the λAB, λAC and λABC terms dropped. It therefore has (a – 1)(b – 1) + (a – 1)(c – … Read More
Basic Concepts There are three conditional independence models (AB, BC), (AC, BC) and (AB, AC). We’ll look at the first of these; the others are similar. The model for (AB, BC) consists of the saturated model with the λAC and λABC terms dropped. It therefore has (a – 1)(c – 1) + (a – 1)(b … Read More
Background In Linear Regression Models for Comparing Means and ANOVA using Regression we studied regression where some of the independent variables were categorical. In this part of the website, we look at log-linear regression, in which all the variables are categorical. Log-linear regression provides a new way of modeling chi-squared goodness of fit and independence problems (see Independence Testing and Dichotomous Variables … Read More
In Independence Testing we use the chi-square test to determine whether two variables are independent. We now look at the same problem using the correlation coefficient with dichotomous dummy variables. Example Example 1: Calculate the point-biserial correlation coefficient for the data in Example 2 of Independence Testing (repeated in Figure 1) using dichotomous variables. Figure … Read More
Objective McNemar’s Test is a paired sample non-parametric test used when the dependent variable is dichotomous. Often, it is used to determine whether there is a significant change in nominal data before and after an event. We begin with an example. Example Example 1: In the BBC program The Doha Debates, 100 people were surveyed … Read More
We review three different measures of effect size for the chi-square goodness-of-fit and independence tests, namely Phi φ, Cramer’s V, and the Odds Ratio. We also describe the effect size for Fisher’s exact test. Phi φ For a 2 × 2 contingency table, phi is the commonly used measure of effect size and is defined … Read More
Introduction When the conditions for Pearson’s chi-square test are not met, especially when one or more of the cells have expi < 5 or with 2 × 2 contingency tables, an alternative approach is to use Fisher’s exact test. Since this method is more computationally intensive, it is best used for smaller samples. 2 × … Read More