Case Study: schizophrenia
Are there any physiological indicators associated with schizophrenia? In a 1990 article, researchers reported the results of a study that controlled for genetic and socioeconomic differences by examining 15 pairs of monozygotic twins, where one of the twins was schizophrenic and the other was not. The researchers used magnetic resonance imaging to measure the volumes (in cm^3) of several regions and subregions of the twins' brains.
Data Snipplet:
Unaffected(twin)Affected(twin) Difference1.941.270.671.441.63-0.191.561.470.09
Output & analysis
One Sample t-test
data: Differenced Data
t = 3.2289, df = 14, p-value = 0.006062
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
0.0667041 0.3306292
sample estimates:
mean of x
0.1986667
References:
Suddath, R.L., Christison, G.W., Torrey, E.F., Casanova, M.F. and Weinberger, D.R. (1990). Anatomical Abnormalities in the Brains of Monozygotic Twins Discordant for Schizophrenia, New England Journal of Medicine 322(12): 789–794.
The fact that the data is paired naturally with twins allows us to take the difference, and account for unobserved confounding variables.
The null hypothesis of the average difference is zero is equivalent to testing the null hypothesis that the mean brain size of a schizophrenic is equal to the mean brain size of a non-schizophrenic individual.
Based on the p-value of the test we can reject the hypothesis that the mean brain size of schizophrenic individuals is equal to non-schizophrenic at the 1% level of significance.
Based on the degrees of freedom in the analysis the sample size is n = 15 differenced observations.
Based on the p-value of the test we fail to reject the hypothesis that the mean brain size of schizophrenic individuals is equal to non-schizophrenic at the 1% level of significance.
The sample mean suggests that the average difference between brain sizes is 0.1986667, and the 95% confidence interval suggests this difference could be as small as 0.0667041 or as large as 0.3306292