Exercise: Head circumference and height

The following graph shows the relationship between head circumference and height in a sample of female healthcare students.

Questions

1. What kind of diagram is this?

Check suggested answer 1.

2. How would you describe the strength of this relationship?

Check suggested answer 2.

3. One of the statistics often calculated for data like these is a correlation coefficient, also known as Pearson’s correlation coefficient or the product moment correlation coefficient, usually denoted by r. What does this tell us?

Check suggested answer 3.

4. What do you think the value of the value of r might be for the relationship between head circumference and height?

Check suggested answer 4.

5. The significance test of the null hypothesis r = 0 in this population gave P < 0.0001. What does this mean and what precisely is it testing? How would you interpret the results of this test?

Check suggested answer 5.

6. What conditions or assumptions do the data have to meet for this test to be valid? Do you think they are met here?

Check suggested answer 6.

7. The program which was used to calculate r printed an approximate 95% confidence interval: 0.24 to 0.54. What does this tell us?

Check suggested answer 7.

8. What conditions or assumptions do the data have to satisfy for this confidence interval to be valid? Do you think these data meet them?

Check suggested answer 8.

9. The following graph shows the regression line for head circumference on height:

The equation of the regression line is:

head circumference = 372 + 0.114 × height

What is a regression line and what does it tell us? In what units are 0.114 and 372 reported?

Check suggested answer 9.

10. The P value is P < 0.0001. What is this testing? What can we conclude from it?

Check suggested answer 10.

11. What assumptions are required for this test? Do you think they are met here? What further information would you like to assess this?

Check suggested answer 11.

12. Would we get a different P value if we carried out the regression of height on head circumference?

Check suggested answer 12.

13. How do the significance tests for the correlation coefficient being zero and the regression slope being zero compare? Are their assumptions different?

Check suggested answer 13.

14. The 95% confidence interval for the slope of the line is 0.067 to 0.161 mm per mm. What does this mean and what can we conclude from it?

Check suggested answer 14.

15. What assumptions do we require for the confidence interval to be valid? Are these different from those required for the confidence interval for the correlation coefficient?

Check suggested answer 15.

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Last updated: 2 March, 2009.