The following are measurements were made on 15 pairs of monozygotic twins, one o

Question

The following are measurements were made on 15 pairs of monozygotic twins, one of whom was affected by schizophrenia (A), and the other of whom was not (U). The measurements are the volumes of the left hippocampus (Cm^3). Compute the differences. D = U - A. and the ranks of the absolute differences. R(|D|) (fill in above) You will notice that 13 of the 15 differences are positive. If p is the probability that a difference is positive, use the sign test to test H_0: p = .5 vs H_1: p > .5. Give the P-value P-value = P_3 (B greaterthanorequalto 13), Now analyze data using the Wilcoxon Signed Rank test. Give the sums of the positive and negative signed ranks. Under the null hypothesis that the differences are symmetrically distributed around 0, find the expected value and variance and standard deviation of T Use statistical software (e.g. Wilcox test in R) to find the exact P-value. P-value = Using the normal approximation, compute the Z-statistic and P-value (using continuity correction) for testing M_d = 0 vs H_1: M_d > 0, where M_D is the median of the differences.

Explanation / Answer

Solution:

(use excel command binom.dist(x,n,p,) )

The p-value is 0.0032, which is smaller than the alpha level of 0.05.

We can reject the null hypothesis and say there is a significant difference.

c)

d) n=15;

e) usinf excel

The p-value is 0.08, which is greater than the alpha level of 0.05.

We fail to reject the null hypothesis and say there is no significant difference.

Pair 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 U 1.94 1.22 1.56 1.58 2.06 1.66 1.75 1.77 1.78 1.92 1.25 1.93 2.04 1.62 2.08 A 1.27 1.63 1.47 1.39 1.93 1.26 1.71 1.87 1.28 1.85 1.02 1.34 2.02 1.59 1.97 D 0.67 -0.41 0.09 0.19 0.13 0.4 0.04 -0.1 0.5 0.07 0.23 0.59 0.02 0.03 0.11 R(|D|) 1 15 9 6 7 4 11 14 3 10 5 2 13 12 8

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