Question 1 The following dataset is taken from Sternberg et

Question 1: The following dataset is taken from Sternberg et al. (1982) Science 216, 1423-1425.

Many theories about the causation of schizophrenia involve changes in the activity of a substance called dopamine in the central nervous system. In this study, 25 hospitalized schizophrenic patients were treated with antipsychotic medication, and after a period of time were classified as either psychotic or nonpsychotic by hospital staff. Samples of cerebrospinal fluid were taken from each patient and assayed for the dopamine b-hydroxlase (DBH) activity (DBH is an enzyme). The data are given below: the units are nmol/(ml)(h)/mg of protein.

Judged nonpsychotic (n₁=15)

Judged psychotic (n₂=10)

.0104

.0150

.0105

.0204

.0112

.0208

.0116

.0222

.0130

.0226

.0145

.0245

.0154

.0270

.0156

.0275

.0170

.0306

.0180

.0320

.0200  

.0200

.0210

.0230

.0252

a) Is there any evidence that there is a difference in variability of DBH activity between the two groups of patients?

b) Is there any evidence that there is a mean difference in DBH activity between the two groups of patients?

c) What is the 95% CI on the nonpsychotic:psychotic ratio of the true variances for the two groups? Demonstrate why it is consistent with your conclusion in a)

Solution