Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

9th Edition

ISBN: 9781337098120

Author: Frederick J Gravetter, Larry B. Wallnau, Lori-Ann B. Forzano

Publisher: Cengage Learning

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Textbook Question

Chapter 12.6, Problem 1LC

Which combination of factors is most likely to produce a large value for the F-ratio and a large value for the η²?

a. Large mean differences and large sample variances
b. Large mean differences and small sample variances
c. Small mean differences and large sample variances
d. Small mean differences and small sample variances

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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Chapter 12 Solutions

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Ch. 12.1 - How many levels are there in a single-factor...Ch. 12.1 - When is the distinction between the testwise alpha...Ch. 12.1 - Which of the following accurately describes the...Ch. 12.2 - For an analysis of variance, the differences...Ch. 12.2 - What is suggested by a large value for the F-ratio...Ch. 12.3 - An analysis of variances produces dfbetween...Ch. 12.3 - An analysis of variance is used to evaluate the...Ch. 12.3 - A research study compares three treatments with n...Ch. 12.4 - A researcher uses analysis of variance to test for...Ch. 12.4 - The following table shows the results of an...

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Solution Summary: The author explains that the correct option is b. Large mean differences and small sample variances. F-ratio is directly proportional to the mean sum of squares between treatments.

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Chapter 12 Solutions