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 by … 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
Introduction We can use the method described in Goodness of Fit to determine whether two sets of data are independent of each other. We organize the data in what are called contingency tables, as described in Example 1. In these cases df = (row count – 1) (column count – 1). Excel worksheet function Excel … Read More
Two-way contingency tables We now define an algorithm that lets us compare two-way tables which have different row and/or column totals. We explain the algorithm using the following example. Example 1: Revise the table in range A5:D7 of the following figure so that the sum of each of the rows is the indicated row total … Read More