   Chapter 12.3, Problem 3LC 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

A researcher conducts an experiment comparing three treatment conditions with a separate sample of n = 8 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Hint: Begin with the values in the df column. To determine

To find: The missing values in the ANOVA table provided.

Explanation

Given info:

The mean of squares within treatments or MSwithin is given as 2 and total sum of squares or SStotal is 62. There are 3 treatment conditions with 8 samples in each treatment.

Calculations:

Degrees of freedom between treatment (dfbetween):

If there are k treatments, then the degrees of freedom between treatments (dfbetween) is:

dfbetween=k1.

Here, number of treatments, k=3.

Substituting the values, we get,

dfbetween=k1=31=2

Degrees of freedom within treatment (dfwithin):

If there are N individuals in the study, then the degrees of freedom within treatment (dfwithin) is: dfwithin=Nk

Substituting the values, we get,

dfwithin=Nk=243=21

Hence,

dftotal=dfwithin+dfbetween=21+2=23

Mean of squares (MS):

The mean of squares of a factor w with corresponding sum of squares SSw is given as:

MSw=SSwdfw

Thus, mean of squares within treatment, MSwithin is:

MSwithin=SSwithindfwithin

SSwithin=MSwithin×dfwithin=2×21

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