Question: Exercise gave data on height and whether or not a student had ever been bullied for 209 secondary school students in England. Among 92 short students, 42 had been bullied. Among 117 students who were not short, 30 had been bullied.

a. For each height category, calculate the risk of having been bullied.

b. What is the relative risk for short students of having been bullied? Write a sentence that interprets this relative risk.

c. What is the increased risk of having been bullied for short students? Write a sentence that interprets this increased risk.

d. Calculate the odds ratio that compares the odds of having been bullied for the short students to the odds for students who are not short. Write a sentence that interprets this ratio.

Exercise: In a study done in England, Voss and Mulligan (2000) collected data on height (short or not) and whether or not the student had ever been bullied in school for 209 secondary school students.

A student was categorized as short if he or she was below the third percentile for height on school entry, but the researchers intentionally sampled in a way that made short students constitute almost half of the sample.

The following table displays a contingency table of the data.

     Height and Bullying in School

                       Ever Bullied?

Height          Yes      No      Total

Short            42       50        92

Not Short      30        87      117

Total            72      137       209

a. Among students in the "short" category, what percentage have ever been bullied?

b. Among students in the "not short" category, what percentage have ever been bullied?

c. Is there a relationship between height and the likelihood of having been bullied? Briefly justify your answer.