Exercise: Head circumference, sex, and height

In a set of measurements made by a group of biomedical science, medical, nursing, physiotherapy, and radiography students, male students had a significantly bigger mean head circumference than female students. Head circumference and height were related. Could it be that the difference in head circumference between the sexes is explained by the difference in height?

The following graph shows a plot of head circumference against height for males and females:

Questions

1. What method could we use to answer the question: is the difference in head circumference between the sexes explained by the difference in height?

Check suggested answer 1.

The regression equation is

Head (mm) = 396 + 0.0957 × height (mm) + 6.80 × sex

where sex = 1 for a female, 2 for a male.

2. What does 6.80 tell us?

Check suggested answer 2.

We can add confidence intervals and P values for the coefficients in this equation:

Head (mm) = 396 + 0.0957 × height (mm) + 6.80 × sex
95% CI 334 to 459 0.0555 to 0.1360 -1.1 to 14.6
P<0.001 P<0.001 P=0.09

3. What can we conclude from this analysis?

Check suggested answer 3.

4. What assumptions about the sample and distributions are needed for this analysis and what could we do to check them?

Check suggested answer 4.

This is the histogram for the residuals, as shown in Answer 4:

5. What can we conclude from these distribution graphs?

Check suggested answer 5.

This is the scatter plot of the residuals against the value predicted by the regression equation, as shown in Answer 4:

6. What can we conclude from the scatter diagram?

Check suggested answer 6.

7. What other assumptions are we making about the relationship between head circumference, height and sex?

Check suggested answer 7.

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Last updated: 2 March, 2009.