Answered: Consider that an analysis of variance…

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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Consider that an analysis of variance is conducted for a research study with three conditions. Each condition has n = 7 participants. It is determined that SS _between = 45 and SS _within = 90. It is also determined that the first condition has a mean of M ₁ = 4, the second condition has a mean of M ₂ = 6, and the third condition has a mean of M ₃ = 8. Which statement below is consistent with the results of this research study, using an alpha of α = .05 and Tukey post-hoc tests?

	a.	M₁, M₂, and M₃ are each statistically different from each other.
	b.	M₁ is statistically different from M₃, but M₂ is not statistically different from M₁ or M₃
	c.	M₂ is statistically different from M₃, but M₁ is not statistically different from M₂ or M₃.
	d.	M₁ is statistically different from M₂ and M₃, but M₂ is not statistically different from M₃

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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