A clinical trial is set up to assess the effects of lithium in treating manic-depressive patients. New patients in an outpatient service are matched according to age, sex, and clinical condition, with one patient receiving lithium and the other a placebo. Suppose the outcome variable is whether or not the patient has any manic-depressive episodes in the next 3 months. The results are as follows: In 20 cases both the lithium and placebo members of the pair have manic-depressive episodes; in 10 cases only the placebo member has an episode (the lithium member does not); in 2 cases only the lithium member has an episode (the placebo member does not); in 36 cases neither member has an episode.
State an appropriate hypothesis to test whether lithium has any effect in treating manic-depressive patients. Why?
Investigate if there is statistically significant difference in treating manic-depressive patients with lithium compared to placebo.
ANSWER::
The chi-square goodness of fit-test is appropriate here because we have a categorical variable.
| observed | expected | O - E | (O - E)² / E |
| 20 | 17.000 | 3.000 | 0.529 |
| 10 | 17.000 | -7.000 | 2.882 |
| 2 | 17.000 | -15.000 | 13.235 |
| 36 | 17.000 | 19.000 | 21.235 |
| 68 | 68.000 | 0.000 | 37.882 |
| 37.88 | chi-square | ||
| 3 | df | ||
| 2.99E-08 | p-value |
The results are statistically significant
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