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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

The following data represent the results from an independent-measures experiment comparing three treatment conditions. Conduct an analysis of variance with α=0.05α=0.05 to determine whether these data are sufficient to conclude that there are significant differences in the means for the treatments.

Treatment A	Treatment B	Treatment C
6	4	13
4	6	11
4	9	7
6	6	10
5	5	9

F-ratio (F-test statistic) =
p-value =
Conclusion:

The data does not provide evidence of a significant difference in the means for the treatments
There is a significant difference in the means for the treatments
I was unable to show the treatments are independent
The data does not provide evidence of a significant correlation for the treatments
I was able to show the treatments are independent
There is a significant correlation in the treatments

The results obtained above were primarily due to the mean for the third treatment being noticeably different from the other two sample means. For the following data, the scores are the same as above except that the difference between treatments was reduced by moving the third treatment closer to the other two samples. In particular, 3 points have been subtracted from each score in the third sample.

Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the F-ratio from above?

Treatment A	Treatment B	Treatment C
6	4	10
4	6	8
4	9	4
6	6	7
5	5	6

F-ratio (F-test statistic) =
p-value =
Conclusion:

There is a significant difference in the means for the treatments
I was able to show the treatments are independent
There is a significant correlation in the treatments
I was unable to show the treatments are independent
The data does not provide evidence of a significant correlation for the treatments
The data does not provide evidence of a significant difference in the means for the treatments

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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