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\Large
\begin{center}
Psychology 407
Assignment \#8
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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:
\bigskip
\normalsize
\begin{tabular}{ccccc}
& & Head position preference & & \\
& Consistent right & Biased right & Biased left & Consistent
left \\
Birth position & & & & \\
Left & 29 & 8 & 8 & 4 \\
Right & 18 & 7 & 12 & 13 \\
\end{tabular}
\bigskip
\Large
a) Test the association between the two attributes using
Pearson's chi-square test of association. Obtain the expected
frequencies under attribute independence and interpret the
discrepancies between ``obtained'' and ``expected''.
\bigskip
b) Test the goodness-of-fit of the column marginal sums against a
uniform distribution.
\bigskip
c) Obtain and interpret Goodman-Kruskals's index of predictive
association for predicting head \emph{from} birth position.
\bigskip
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.
\bigskip
\begin{tabular}{ccc}
& Cold & No Cold \\
Placebo & 31 & 109 \\
Ascorbic Acid & 17 & 122 \\
\end{tabular}
\bigskip
a) Test the association using Pearson's chi-square test; obtain
the expected values of the cell frequencies under independence.
\bigskip
b) What is the four-fold point correlation?
\bigskip
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:
\bigskip
\begin{tabular}{ccc}
& Psychotics & Neurotics \\
Suicidal feelings & 2 & 6 \\
No suicidal feelings & 18 & 14 \\
\end{tabular}
\bigskip
a) Carry out a test of association using Fisher's exact test.
How does the p-value compare to the chi-square approximation?
\bigskip
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 one-to-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:
\bigskip
\begin{tabular}{cccc}
& & Depersonalized & \\
& & Not recovered & Recovered \\
& Recovered & 5 & 14 \\
Not depersonalized & & & \\
& Not Recovered & 2 & 2 \\
\end{tabular}
\bigskip
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 \emph{and} the exact
version based on the binomial distribution.
\bigskip
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):
\bigskip
\begin{tabular}{ccccc}
& & & 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 \\
\end{tabular}
\bigskip
a) Obtain Cohen's Kappa statistic for these data and test its
significance against zero using the hypothesis of independence
between the raters.
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