6.48 Coffee and Depression: Researchers conducted a study investigating the relationship between caffeinated coffee consumption and risk of depression in women. They collected data on 50,739 women free of depression symptoms at the start of the study in the year 1996, and these women were followed through 2006. The researchers used questionnaires to collect data on caffeinated coffee consumption, asked each individual about physician-diagnosed depression, and also asked about the use of antidepressants. The table below shows the distribution of incidences of depression by amount of caffeinated coffee consumption. (M. Lucas et al, 2011)
| ≤ 1 cup/week | 2-6 cups/week | 1 cup/day | 2-3 cups/day | ≥ 4 cups/day | Total | |
|---|---|---|---|---|---|---|
| Clinical Depression: Yes | 670 | 373 | 905 | 564 | 95 | 2607 |
| Clinical Depression: No | 11545 | 6244 | 16329 | 11726 | 2288 | 48132 |
| Total | 12215 | 6617 | 17234 | 12290 | 2383 | 50739 |
a) What type of test is appropriate for evaluating if there is an association between coffee intake and depression?
b) Write the hypotheses for the test you identified in part a)
c) Calculate the overall proportion of women who do and do not suffer from depression:
(round to four decimal places)
Depression:
No Depression:
d) Identify the expected count for the cell corresponding to individuals with clinical depression and who drink 2-6 cups of coffee per week. Then calculate the contribution of this cell to the test statisitc, i.e. (Observed - Expected)2/Expected
Observed:
Expected:
Contribution to test statistic:
e) The test statistic for the hypothesis test is χ2=20.93. What is the p-value?
f) What is the conclusion of this test?