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Essentials of Statistics for the B...

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

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

To create the following data we started with the same sample means and variances that appeared in problem 10 but increased the sample size to n = 25.

M= 2 M=3 M=4
n=25 n=25 n=25
T=50 T=75 T=100
S2= 2.67 S2=2.00 s2=1.33

a.     Predict how the increase in sample size should affect the F-ratio for these data compared to the f-ratio in problem 10. Use an ANOVA to check your prediction. Note: Because the samples are all the same size. MSwithin is the average of the three sample variances.

b. Predict how the increase in sample size should affect the value of η 2 for these data compared to the η 2 in problem 10. Calculate η 2 to check your prediction.

a.

To determine

To-predict: The effect on size of the F-ratio after increase in sample size.

To determine: There are any significant mean differences between treatments.

Explanation

Given info:

The data represents the summary statistics.

Treatment
I II III
n=25 n=25 n=25
M=2 M=3 M=4
T=50 T=75 T=100
s2=2.67 s2=2 s2=1.33
SS=64.08 SS=48 SS=31.92

Also, N=75 and G=225.

Level of significance is α=0.05.

Calculation:

On increasing the sample size, the sum of squares between treatments increases, hence numerator of the F-ratio increases. Therefore, size of F-ratio increases and chances to reject the null hypothesis increases.

Let k represents the numbers of treatments. Then,

k=3

Then, degrees of freedom corresponding to SSbetween are:

dfbetween=k1=31=2

Then, degrees of freedom corresponding to SSwithin are:

dfwithin=Nk=753=72

SSwithin is calculated as:

SSwithin=SS=64

b.

To determine

To predict: The effect of increase in sample size on the effect size η2 for the study.

To determine: The effect size η2 for the study.

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