15.45 Gender bias, poor growth, and hypothesis testing: Grimberg et al., (2005) wondered whether gender biases were evident in referrals of children for poor growth. They believed that boys were more likely to be referred even when there was no problem—which is bad for boys because families of short boys might falsely view their height as a medical problem. They also believed that girls were less likely to be referred even when there was a problem—which is bad for girls because real problems might not be diagnosed and treated. They studied all new patients at the Children’s Hospital of Philadelphia Diagnostic and Research Growth Center who were referred for potential problems related to short stature. Of the 182 boys who were referred, 27 had an underlying medical problem, 86 did not but were below norms for their age, and 69 were of normal height according to growth charts. Of the 96 girls who were referred, 39 had an underlying medical problem, 38 did not but were below norms for their age, and 19 were of normal height according to growth charts.

a. How many variables are there in this study? What are the levels of any variable you identified?

b. Which hypothesis test would be used to analyze these data? Justify your answer.

c. Conduct the six steps of hypothesis testing for this example.

d. Calculate the appropriate measure of effect size. According to Cohen’s conventions, what size effect is this?

e. Report the statistics as you would in a journal article.

f. Draw a table that includes the conditional proportions for boys and for girls. g. Create a graph with bars showing the proportions for all six conditions. h. Among only children who are below height norms, calculate the relative risk of having an underlying medical condition if one is a boy as opposed to a girl. Show your calculations. i. Explain what we learn from this relative risk.

j. Now calculate the relative risk of having an underlying medical condition if one is a girl. Show your calculations. k. Explain what we learn from this relative risk. l. Explain how the calculations in parts (h) and (j) provide us with the same information in two different ways. m. The printout from SPSS software at the bottom of the previous page depicts the data for the six cells. For each cell, there is an observed frequency (count), expected frequency (expected count), and adjusted standardized residual (adjusted residual). For boys, what are the observed and expected frequencies for having an underlying medical condition? n. For boys, what is the adjusted standardized residual for those with an underlying medical condition? What does this number indicate? If you used an adjusted standardized residual criterion of 2 (regardless of the sign), for which cells would you conclude that the difference between observed frequency and expected frequency is greater than you would expect if the two variables were independent? What if you used an adjusted standardized residual criterion of 3 (regardless of the sign)? Are the results different from those using a criterion of 2? If yes, explain how.