Question

III. In a psychiatric study of families of schizophrenic children two Rorshach scores of the mothers (M, and M,) and fathers ( F, F,) were of particular import. The observed values of these scores for parents of nl=10 psychotic adolescents and n2=10 normal control children of similar age and economic status are given below:

Schizophrenia				control
M1	M2	F1	F2	M1	M2	F1	F2
30	35	25	33	20	15	26	25
21	41	15	21	11	3	18	19
27	32	25	34	7	2	11	8
35	34	31	36	21	15	24	22
20	37	14	21	15	11	17	13
23	38	19	25	13	12	20	15
28	27	26	30	22	13	22	19
32	42	29	37	5	3	9	12
26	36	27	33	21	13	20	19
29	35	24	32	14	12	10	8

 Analyze this data.

Answer 1

Performing student t test on test and control would tell us the severity of schizophrenic.

In all the four cases estimated mean value of test group is greater than control group. All the t-test are significant as p < 0.05.

# mean of test group is 2 times the mean of control group

### R Code for t test #####

t_c <-read.csv('t_c.csv')

## M1
t.test(t_c$M1, t_c$M1C)

# Welch Two Sample t-test
#
# data: t_c$M1 and t_c$M1C
# t = 5.0001, df = 17.057, p-value = 0.0001085
# alternative hypothesis: true difference in means is not equal to 0
# 95 percent confidence interval:
# 7.053469 17.346531
# sample estimates:
# mean of x mean of y
# 27.1 14.9

## M2
t.test(t_c$M2, t_c$M2C)

# Welch Two Sample t-test
#
# data: t_c$M2 and t_c$M2C
# t = 12.132, df = 17.471, p-value = 6.101e-10
# alternative hypothesis: true difference in means is not equal to 0
# 95 percent confidence interval:
# 21.32257 30.27743
# sample estimates:
# mean of x mean of y
# 35.7 9.9

## F1
t.test(t_c$F1, t_c$F1C)

# Welch Two Sample t-test
#
# data: t_c$F1 and t_c$F1C
# t = 2.2267, df = 17.968, p-value = 0.03899
# alternative hypothesis: true difference in means is not equal to 0
# 95 percent confidence interval:
# 0.3270459 11.2729541
# sample estimates:
# mean of x mean of y
# 23.5 17.7

## F2
t.test(t_c$F2, t_c$F2C)

# Welch Two Sample t-test
#
# data: t_c$F2 and t_c$F2C
# t = 5.4651, df = 17.993, p-value = 3.436e-05
# alternative hypothesis: true difference in means is not equal to 0
# 95 percent confidence interval:
# 8.741053 19.658947
# sample estimates:
# mean of x mean of y
# 30.2 16.0