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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

The following data are from an experiment comparing three different treatment conditions:

A B C  
0 1 2 N = 15
2 5 5 ΣX2 = 354
1 2 6  
5 4 9  
2 8 8  
T = 10 T = 20 T = 30  
SS = 14 SS = 30 SS = 30  
  1. a. If the experiment uses an independent-measures design, can the researcher conclude that the treatments are significantly different? Test at the .05 level of significance.
  2. b. If the experiment is done with a repeated-measures design, should the researcher conclude that the treatments are significantly different? Set alpha at .05 again.
  3. c. Explain why the analyses in parts a and b lead to different conclusions.

a.

To determine

To find: The significance of mean difference using independent measures ANOVA with α=0.05

Explanation

Given info: The data is given is question

A B C

 

N=15X2=354

n=5 n=5 n=5
T=10 T=20 T=30
SS=14 SS=30 SS=30

Calculation:

Step 1:

The null and alternative hypotheses are:

Null hypothesis:

  H0:μ1=μ2=μ3,

Where μ1μ2μ3 are the means of the 3 treatments.

Alternate hypothesis:

Ha: At least one treatment mean is different.

Step 2:

Compute the degrees of freedom (df) for the between treatment effects, within treatment effects and total and corresponding sum of squares (SS).

Now, it is known that, for a given sample size, the degrees of freedom (df) is:

df=(number of units)1.

Thus,

dftotal=N1=151=14

The number of treatments, k=3. Thus,

dfbetween=k1=31=2

As within treatments degrees of freedom, dfwithin=dftotaldfbetweentreatment, thus,

dfwithin=dftotaldfbetweentreatment=142=12

With α=0.05 and df=(2,12) critical value from table is CV=3.88

Step 3:

Compute F-ratio.

The total sum of squares is:

SStotal=X2G2N.

The within treatment sum of squares is:

SSwithintreatment=SSinsideeachtreatment.

The within treatment sum of squares is:

SSbetween=T2nG2N

b.

To determine

To find: The significance of mean difference using repeated measures ANOVA with α=0.05

c.

To determine

To find: Why the results of analysis different in part (a) and part (b)

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