Overview We describe the testing of 2 × 2 contingency tables for independence, including the chi-square test and Fisher and Boschloo exact tests. We also describe the 2 × 2 Contingency Table Testing data analysis tool. A 2 × 2 contingency table takes the following form Chi-square Test The expected values mij in the usual … Read More
In Independence Testing we show how to test independence using a chi-square test. We now show how to perform such a test when there is missing data (provided the data is missing at random). Example Example 1: Impute the missing data in the contingency table shown in Figure 1. Figure 1 – Contingency Table with … Read More
Example Example 1: Determine which of the log-linear models is the best fit for the data in Example 2 of Independence Testing. Figure 1 summarizes the main findings from the various analyses we have conducted (as described in Saturated, Independence and Other Models for two-way contingency tables). Figure 1 – Summary of the fit of all the … Read More
In this section we re-examine the two-way contingency tables studied in Independence Testing using the following log-linear regression model: where all the xij are dummy variables coded to represent categorical variables. In addition, we also consider more complicated models that contain factors consisting of interactions between the same variables, as described in the sections listed below, and the … Read More
Example Example 1: Now let us return to the problem we posed in Example 1 of Three-way Contingency Tables, namely to find the most parsimonious model that fits the data. Figure 1 summarizes the key results for all 18 models. Figure 1 – Summary of all log-linear regression models From Figure 1, we see that … Read More
Basic Concepts Log-linear models for two-way contingency tables, only provide another way of looking at the chi-square analyses studied in Independence Testing. Since the traditional chi-square test is not available for three-way tables, log-linear models become an important way to analyze such tables. We now extend the approach used in Two-way Contingency Tables to three-way … Read More
Basic Concepts The saturated model for Example 1 of Three-way Contingency Tables takes the form: where terms involving C and G require 2 – 1 = 1 coefficient and terms involving T require 3 – 1 = 2 coefficients. Thus terms involving CG, CT, GT and CGT require 1 ∙ 1 = 1, 1 ∙ … Read More
Basic Concepts The saturated and independence models are the only log-linear models for two-way contingency tables that use both variables. There are, however, a number of other models. The complete list of models is given in Figure 1. Figure 1 – Model types for two-way contingency tables Here A and B are the names for … Read More
We now turn our attention to modeling the case where we presume that the variables are independent. This is the situation we studied when using the chi-square distribution to test two-way contingency tables in Independence Testing. Example Example 1: Create an independence log-linear model for the data in Example 2 of Independence Testing. We repeat … Read More
We begin by investigating the saturated model, which accounts for all the possible variables. We do this by reexamining Example 2 of Independence Testing using a log-linear approach. Example Example 1: Create a saturated log-linear model for the data in Example 2 of Independence Testing The data for the 150 patients are again summarized in the contingency … Read More