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.