Psychology 407 Assignment #8

I. Goodwin and Michael (1981) performed a study of newborn infants, recording birth position (left or right) and head position preference (whether the child consistently looked right, had a bias toward looking right, had a bias toward looking left, or consistently looked left). The observed frequencies are shown below:

Head position preference

Consistent right Biased right Biased left Consistent left

Birth position

Left  29  8  8  4
Right  18  7  12  13

a) Test the association between the two attributes using Pearson’s chisquare test of association. Obtain the expected frequencies under attribute independence and interpret the discrepancies between “obtained” and “expected”.

b) Test the goodness-of-fit of the column marginal sums against a uniform distribution.

c) Obtain and interpret Goodman-Kruskals’s index of predictive association for predicting head from birth position.

II. In a review of the evidence regarding the therapeutic value of ascorbic acid (Vitamin C) for treating the common cold, Pauling (1971) describes a 1961 French study involving 279 skiers during two periods of 5–7 days. The study was double-blind with one group of 140 subjects receiving a placebo while a second group of 139 received 1 gram of ascorbic acid per day. Of interest is the relative occurrence of colds for the two groups where the data are as follows.

Cold No Cold
Placebo 31 109
Ascorbic Acid 17  122

a) Test the association using Pearson’s chi-square test; obtain the expected values of the cell frequencies under independence. b) What is the four-fold point correlation?

III. For the present purposes, assume mental patients can be classified as psychotics or neurotics. A psychiatrist, while studying the symptoms of a sample of 20 from each of these populations found that six patients in the neurotic group had suicidal feelings and two in the psychotic group:

Psychotics Neurotics
Suicidal feelings  2  6
No suicidal feelings  18  14

a) Carry out a test of association using Fisher’s exact test. How does the p-value compare to the chi-square approximation?

IV. A psychiatrist wished to assess the effect of the symptom “depersonalization” of the prognosis of depressed patients. Twenty-three depressed patients, who were diagnosed as being “depersonalized”, were matched oneto-one for age, sex, duration of illness, and on certain personality variables, with 23 depressed patients who were diagnosed as not being “depersonalized”. The number of pairs of patients from the two samples who, on discharge after a course of ECT, were diagnosed as “recovered” or “not recovered” are given below:

Depersonalized

Not recovered Recovered
Recovered 5 14

Not depersonalized

Not Recovered  2  2

a) Using McNemar’s test of correlated proportions, test the equality of the “recovered” proportions for the two types of patients. Carry out the test using the chi-square approximation and the exact version based on the binomial distribution.

V. In viewing a set of video tapes of 50 couples involved in marital counseling, two raters assigned the couples to one of three behavioral categories based on the interactions observed. The data turned out as follows (C_{1}, C_{2}, and C_{3} denote the behavioral categories):

rater b

C_{1} C_{2} C_{3}
C_{1} 14  2  3
rater a C_{2} 0  10  1
C_{3} 6  2  12

a) Obtain Cohen’s Kappa statistic for these data and test its significance against zero using the hypothesis of independence between the raters.