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Chapter 13: Q.13.22 (page 532)

Discuss two methods for checking the assumptions of normal populations and equal standard deviations for a one-way ANOVA.

Short Answer

Expert verified

The condition of normality and equal standard deviations is met if the large sample deviation to small sample deviation ratio is less than two.

Step by step solution

01

Given Information

Consider ANOVA in one direction.

Take the residual analysis method into consideration.

02

Explanation

The residual is computed for each value in a one-way ANOVA. The difference between the actual and expected values is known as the residual.

The normal probability plot of the residual is approximately linear if normality and equal standard deviations are met. The residuals plot should be horizontal band centered and symmetric about the horizontal axis when compared to the sample means.

Consider a normal probability plot of the sample data, which is useful for detecting normality variations.

It's tough to check for equal standard deviations when the sample size is tiny. The condition of normality and equal standard deviations is satisfied if the large sample deviation to small sample deviation ratio is less than two.

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Most popular questions from this chapter

Regarding one-way ANOVA, fill in the blanks in each of Exercises 13.15-13.17
13.15 A measure of variation among the sample means is called the ------ The mathematical abbreviation for it is--------

Staph Infections. In the article "Using EDE, ANOVA and Regression to Optimize Some Microbiology Data" (Journal of Statistics Education, Vol. 12, No. 2, online), N. Binnie analyzed bacteria culture data collected by G. Cooper at the Auckland University of Technology. Five strains of cultured Staphylococcus aureus bacteria that cause staph infections were observed for 24hours at 27oC. The following table reports bacteria counts, in millions, for different cases from each of the five strains.

At the 5%significance level, do the data provide sufficient evidence to conclude that a difference exists in mean bacteria counts among the five strains of Staphylococcus aureus? (Note: T1=104,T2=129, T3=185,T4=98,T5=194,Σx2i=25,424.)

In one-way ANOVA,

a. list and interpret the three sums of squares.

b. state the one-way ANOVA identity and interpret its meaning with regard to partitioning the total variation among all the data.

For what is one-way ANOVA used?

Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10, 12, and 15. Determine the degrees of freedom for the F-statistic.
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