   Chapter 12, Problem 18P 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 developmental psychologist is examining the development of language skills from age 2 to age 4. Three different groups of children are obtained, one for each age, with n = 16 children in each group.Each child is given a language-skills assessment test. The resulting data were analyzed with an ANOVA to test for mean differences between age groups. The results of the ANOVA are presented in the following table. Fill in all missing values. To determine

To find: The missing values.

Explanation

Given info:

The data represents the three age groups from age 2 to 4 with sample of size n=16.

Calculation:

Here, k represents the numbers of treatments, n represents numbers of observations in each treatment and N represents the total numbers of observations. Then,

k=3,n=16.

The total number of observations N is obtained below:

N=k×n=3×16=48

From the given table:

SStotal=200,SSbetween=20

Degrees of Freedom:

dfbetween=k1=31=2

dfwithin=Nk=483=45

A total degrees of freedoms is:

dftotal=dfbetween+dfwithin=2+45=47

SSwithin is obtained as:

SSwithin=SStotalSSbetween=20020=180

MSwithin is obtained as:

MSwithi

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