   Chapter 12, Problem 3P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Why should you use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions?

To determine
Reasons to use ANOVA instead of several t tests.

ANOVA uses variances for sample means which leads to a single value for more than two treatments as well while there are large numbers of differences of means for t tests if there are more than two treatments. Also, ANOVA reduces the experimental type-I error.

Explanation

Given info:

An experiment consists of three or more treatment conditions.

Justification:

When an experiment consists of more than three treatments, then t tests to evaluate mean differences cannot be used because t tests use difference of means in the statistic to make conclusions whether population means differ or not. If more than two treatments are available, then numbers of differences of means of treatments are more than one. So, more than one difference of sample mean cannot be used in the t statistic formula.

On the other hand, ANOVA uses variances for sample means which leads to a single value for more than two treatments.

Also, there can be large experimental type-I error if t tests are used to compare differences for means because numbers of tests would be large.

Conclusion:

ANOVA uses variances for sample means which leads to a single value for more than two treatments as well while there are large numbers of differences of means for t tests if there are more than two treatments. Also, ANOVA reduces the experimental type-I error.

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