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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

Explain why the F-ratio is expected to be near 1.00 the null hypothesis is true.

To determine

To explain: The reason for the F-ratio being nearby 1 when the null hypothesis is true.

Answer

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. In such cases, F ratio gets balanced and takes a value near to 1.

Explanation

The null hypothesis in ANOVA is: There is no treatment effect.

The F ratio is given as:

F=(systematic treatments effects)+(random unsystematic differences)random unsystematic differences

When null hypothesis is true which means treatment effects are null or not significant, then F ratio is:

F=0+(random unsystematic differences)random unsystematic differences=random unsystematic differencesrandom unsystematic differences

When the treatment effect is null, then numerator and denominator in F ratio will have the same source of variability. Since, F ratio will be 1.

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