111 Heights of grade school repeaters. The Archives of Disease in Childhood (Apr. 2000) conducted a study conducted a of whether height influences a child’s progression through elementary school. Within each grade, Australian schoolchildren were divided into equal thirds (tertiles) based on age (youngest third, middle third, and oldest third). The researchers compared the average heights of the three groups, using an analysis of variance. (All height measurements were standardized with z -scores.) A summary of the results for all grades combined, by gender, is shown in the table at the bottom of the page.

a. What is the null hypothesis for the ANOVA of the boys’ data?

b. Interpret the results of the test, part a . Use a = .05.

c. Repeat parts a and b for the girls’ data.

d. Summarize the results of the hypothesis tests in the words of the problem.

e. The three height means for boys were ranked with the Bonferroni method at a = .05. The line in the summary table connects those means which are not significantly different. Which tertile has the smallest mean height?

f. What is the experimentwise error rate for the inference made in parts e ? Interpret this value.

g. The researchers did not perform a Bonferroni analysis of the height means for the three groups of girls.

Explain why not.

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Summary information for Exercise 111 Sample Size Boys Girls 1439 1409 Youngest Tertile Mean Height 0.33 0.27 Middle Tertile Oldest Tertile Mean Height Mean Height F-Value p-Value 0.33 0.18 0.16 0.21 4.57 0.01 0.85 0.43 Based on Wake, M., Coghlan, D., and Hesketh, K. "Does height influence progression through primary school grades?" The Archives of Disease in Childhood, Vol. 82, No. 4, Apr. 2000 (Table 2), pp. 297-301.