Chapter 12 – Relationships Between Categorical Variables
Categorical variables are shown in contingency variables because they cover the contingency
combinations for both variables.
It is hard to make comparisons from contingency tables. We can calculate conditional percentages for
the response variable. Response variable number/total response variable people. The rate is the number
of individuals per hundred, percentage is rate/100.
There are two ways to express chance. Proportion of the total and odds (involves the other category). If
40% of 1000 carry a gene then the proportion is 0.40. The probability is 0.40. The risk is 0.40. The odds is
4 to 5 or 2 to 3.
Percentage = # with trait/total x 100
Proportion = # with trait/total
Probability = # with trait/total
Risk = # with trait/total
Odds = # with trait/# without trait “to 1”
Proportion Odds = p/1-p “to 1”, p=proportion
Odds Proportion = a/(a+b), a to b
The baseline risk is the risk without the treatment or behaviour. For the aspirin/heart attack example
the baseline risk is the risk of a heart attack without taking aspirin. The baseline risk can be hard to find.
Placebo/Control groups give us a baseline risk.
The relative risk of an outcome for two categories of an explanatory variable is the ratio of risk for each
category. It is often expressed as a multiple. Relative risk of one means the risk is the same for both