StatisticsChapter 19Categorical outcomes: chi-square and loglinear analysisAnalysing categorical data Sometimes we want to predict categorical outcome variables. We want to predict into which category an entity falls. With categorical variables we can’t use the mean or any similar statistic because the mean of a categorical variable is meaningless: the numeric values you attach to different categories are arbitrary, and the mean of those numeric values will depend on how many members each category has.When we’ve measured only categorical variables, we analyse the number of things that fall into each combination of categories (the frequencies).Pearson’s chi-square test To see whether there’s a relationship between two categorical variables we can use the Pearson’s chi-square test.This statistic is based on the simple idea of comparing the frequencies you observe in certain categories to the frequencies you might expect to get in those categories by chance.X2 = Σ(observedij-modelij)2 / modeliji represents the rows in the contingency tablej represents the columns in the contingency table.As model we use ‘expected frequencies’.To adjust for inequalities, we calculate frequencies for each cell in the table using the column and row totals for that cell.By doing so we factor in the total number of observations that could have contributed to that cell.Modelij = Eij = (row totali x column...