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Chapter 13: Q. 13.18 (page 532)

13.18 Explain the logic behind one-way ANOVA.

Short Answer

Expert verified

One way ANOVA is applied to two groups, it gives the identical results as t-test.

Step by step solution

01

Given information

To explain the logic behind one-wayANOVA.

02

Explanation

The ANOVA stands for analysis of variance.
It calculates the difference in means between more than two groups.
The core principle behind a one-way ANOVAis that it compares the means of many groups in the same way that a t-test compares the means of two independent groups.
When a one-way ANOVAis used on two groups, the findings are equivalent to a t-test.

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Most popular questions from this chapter

In one-way ANOVA, what is the residual of an observation?

Consider the following hypothetical samples

a. Obtain the sample mean and sample variance of each of the three samples.

b. Obtain SST, SSTR and SSE by using the defining formulas and verify that the one-way ANOVA identity holds.

c. Obtain SST, SSTR and SSE by using the computing formulas.

d. Construct the one-way ANOVA table.

Explain the reason for the word variance in the phrase analysis of variance.

Popular Diets. In the article "Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction" (Journal of the American Medical Association, Vol. 293, No. 1, Pp, 43-53), M. Dansinger et al. conducted a randomized trial to assess the effectiveness of four popular diets for weight loss. Overweight adults with an average body mass index of35and ages22-72years participated in the randomized trial for 1 year. The weight losses, in kilograms, based on the results of the experiment are given on the WeissStats site. Negative losses are gains. WW=Weight Watchers.

a. Obtain individual normal probability plots and the standard deviation of the samples.

b. Perform a residual analysis.

c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so. also do parts (d) and (e).

d. Use a one-way ANOVA test to decide, at the 5%significance level, Whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations fewer than the samples were taken.

e. Interpret your results from part (d)

We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, F, is too large. Why is the null hypothesis rejected only when F is too large?
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