11.3.3 - Relative Risk

A chi-square test of independence will give you information concerning whether or not a relationship between two categorical variables in the population is likely. As was the case with the single sample and two sample hypothesis tests that you learned earlier this semester, with a large sample size statistical power is high and the probability of rejecting the null hypothesis is high, even if the relationship is relatively weak. In addition to examining statistical significance by looking at the p value, we can also examine practical significance by computing the relative risk.

In Lesson 2 you learned that risk is often used to describe the probability of an event occurring. Risk can also be used to compare the probabilities in two different groups. First, we'll review risk, then you'll be introduced to the concept of relative risk.

The risk of an outcome can be expressed as a fraction or as the percent of a group that experiences the outcome.

Risk
\(Risk=\dfrac{n\;with\;outcome}{total\;n}\)

Examples of Risk Section

Asthma

60 out of 1000 teens have asthma. The risk is \(\frac{60}{1000}=.06\). This means that 6% of all teens experience asthma.

Flu

45 out of 100 children get the flu each year. The risk is \(\frac{45}{100}=.45\) or 45%

Relative Risk
Relative risk compares the risk of a particular outcome in two different groups.
Relative Risk
\(Relative\ Risk=\dfrac{Risk\ in\ Group\ 1}{Risk\ in\ Group\ 2}\)

Thus, relative risk gives the risk for group 1 as a multiple of the risk for group 2.

Examples of Relative Risk Section

Asthma

Suppose, 7% of teenage girls have asthma compared to 5% of teenage boys with asthma. Using the females as group 1, what is the relative risk for girls compared to boys?

  •  \(Relative\;risk=\dfrac{7 \%}{5 \%}=1.4\) 

The risk of asthma is 1.4 times as great for teenage girls as it is for teenage boys.

Flu

Suppose that the risk of a child getting the flu this year is .45 and the risk of an adult getting the flu this year is .10. What is the relative risk of children compared to adults?

  • \(Relative\;risk=\dfrac{.45}{.10}=4.5\)

Children are 4.5 times more likely than adults to get the flu this year.

Caution Section

Watch out for relative risk statistics where no baseline information is given about the actual risk. For instance, it doesn't mean much to say that beer drinkers have twice the risk of stomach cancer as non-drinkers unless we know the actual risks. The risk of stomach cancer might actually be very low, even for beer drinkers. For example, 2 in a million is twice the size of 1 in a million but is would still be a very low risk. This is known as the baseline with which other risks are compared.