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Name: Researchers have sought to examine the effect of various types of musi
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Description: Researchers have sought to examine the effect of various types of music on agitation levels in patients who are in the early and middle stages of Alzheimer's disease. Patients were selected to participate in the study based on their stage of Alzheime

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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Researchers have sought to examine the effect of various types of music on agitation levels in patients who are in the early and middle stages of Alzheimer's disease. Patients were selected to participate in the study based on their stage of Alzheimer's disease. Three forms of music were tested: Easy listening, Mozart, and piano interludes. While listening to music, agitation levels were recorded for the patients with a high score indicating a higher level of agitation. Scores are recorded below.

Group

Piano Interlude

Mozart

Easy Listening

Early Stage Alzheimer's

21
24
22
18
20

Mean=21.0

9
12
10
5
9

Mean=9.0

29
26
30
24
26

Mean=27.0

Middle Stage Alzheimer's

22
20
25
18
20

Mean=21.0

14
18
11
9
13

Mean=13.0

15
18
20
13
19

Mean=17.0

Complete the following ANOVA table.

Source	df	SS	MS	F
Type of Music	2	740
Degree of Alzheimer's	1	30
Interaction	2	260
Error	24	178
Total	29	1208

Are there any significant main effects or an interaction effect?
Interpret your answer.

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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