Are any physiological indicators associated with schizophrenia? Early studies, based largely on post- mortem analysis, suggest that the sizes of certain areas of the brain may be different in persons afflicted with schizophrenia than in others. Confounding variables in these studies, however, clouded the issue considerably. In a 1990 article, researchers reported the results of a study that controlled for genetic and socioeconomic differences by examining 15 pairs of identical twins, where one of the twins was schizophrenic and the other was not. The twins were located through an intensive search through- out Canada and the United States (Data from R. L. Suddath et al., "Anatomical Abnormalities in the Brains of Monozygotic Twins Discordant for Schizophrenia," New England Journal of Medicine 322(12) (1990):789-93.). The researchers used magnetic resonance imaging (MRI) to measure the volumes (in cm³) of several re- gions and subregions inside the twins' brains. The table presents data based on the reported summary statistics from one subregion, the left hippocampus. Unaffected Affected diff 1.27 0.67 1.63 -0.19 1.47 0.09 1.39 0.19 1.93 0.13 1.26 0.40 1.71 0.04 1.67 0.10 1.28 0.50 1.85 0.07 1.02 0.23 1.34 0.59 2.02 0.02 1.59 0.03 1.97 0.11 1.94 1.44 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 Mean 1.7587 1.5600 0.1987 SD 0.2424 0.3013 0.2383

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Construct a 95% confidence interval for the mean difference in volumes of the left hippocampus between
the unaffected and the affected individuals.

Are any physiological indicators associated with schizophrenia? Early studies, based largely on post-
mortem analysis, suggest that the sizes of certain areas of the brain may be different in persons afflicted
with schizophrenia than in others. Confounding variables in these studies, however, clouded the issue
considerably. In a 1990 article, researchers reported the results of a study that controlled for genetic
and socioeconomic differences by examining 15 pairs of identical twins, where one of the twins was
schizophrenic and the other was not. The twins were located through an intensive search through-
out Canada and the United States (Data from R: L. Suddath et al., "Anatomical Abnormalities in the Brains
of Monozygotic Twins Discordant for Schizophrenia," New England Journal of Medicine 322(12) (1990):789-93.). The
researchers used magnetic resonance imaging (MRI) to measure the volumes (in cm³) of several re-
gions and subregions inside the twins' brains. The table presents data based on the reported summary
statistics from one subregion, the left hippocampus.
Unaffected Affected diff
1.94
1.27 0.67
1.44
1.63 -0.19
1.56
1.47 0.09
1.58
1.39
0.19
2.06
1.93 0.13
1.66
1.26 0.40
1.75
1.71
0.04
1.77
1.67 0.10
1.78
1.28 0.50
1.92
1.85
0.07
1.25
1.02 0.23
1.93
1.34
0.59
2.04
2.02 0.02
1.62
1.59 0.03
2.08
1.97 0.11
Mean 1.7587
1.5600 0.1987
SD 0.2424 0.3013 0.2383
1

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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