# Zach’s facts

Zach’s facts have been extracted from the book to remind you of the key concepts you and Zach have learned in each chapter.

Zach’s Facts 13.1 Relationships between categorical variables

• If you want to test the relationship between two categorical variables you can do this with Pearson’s chi-square test or the likelihood ratio statistic.

• Check to make sure that no expected frequencies are less than 5 (in a 2 × 2 contingency table) or that none are less than 1 and no more than 20% are less than 5 in bigger contingency tables.

• Look at the contingency table to work out what the relationship between the variables is: look out for significant standardized residuals (values outside of ±1.96), and columns that have different letters as subscripts (this indicates a significant difference).

• Calculate the odds ratio.

• Report the c2 statistic, the degrees of freedom, sample size, the significance value, and the odds ratio. Also report the contingency table.

Zach’s Facts 13.2 Correlations

• The correlation coefficient measures the linear relationship between two variables.

• A coefficient of +1 indicates a perfect positive relationship, a coefficient of −1 indicates a perfect negative relationship, and a coefficient of 0 indicates no linear relationship at all.

• Values of ±0.1 represent a small effect, ±0.3 is a medium effect and ±0.5 is a large effect. However, interpret the size of correlation within the context of the research you’ve done, rather than blindly referring to these benchmarks.

• The percentage bend correlation is a robust variant of the correlation coefficient.