Essentials Of Statistics For The Behavioral Sciences
Essentials Of Statistics For The Behavioral Sciences
9th Edition
ISBN: 9781337273312
Author: GRAVETTER, Frederick J., Wallnau, Larry B., Forzano, Lori-ann B.
Publisher: Cengage Learning,
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 12, Problem 22P

To create the following data we started with the same sample means and variances that appeared in problem 21 but doubled the sample size to n = 10.

Chapter 12, Problem 22P, To create the following data we started with the same sample means and variances that appeared in

a. Predict how the increase in sample size should affect the F-ratio for these data compares to the values obtained in problem 21. Use an ANOVA with a – .05 to check your prediction. Note: Recause the sample 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’ for these data compared to the η’ in problem 21. Calculate η’ to check your prediction.

a.

Expert Solution
Check Mark
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.

Answer to Problem 22P

On increasing the sample size, the size of F-ratio increases. There are significant mean differences between the treatments.

Explanation of Solution

Given info:

Treatment
I II III
n=10 n=10 n=10 N=30
M=1 M=5 M=6 G=120
T=10 T=50 T=60 X2=890
s2=9 s2=10 s2=11
SS=81 SS=90 SS=99

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=303=27

SSwithin is calculated as:

SSwithin=SS=81+90+99=270

Sum of squares between treatments is given as:

SSbetween=T2nG2N=(10)210+(50)210+(60)210(120)230=10+250+360480=140

F-ratio is calculated as:

F=SSbetweendfbetweenSSwithindfwithin=140227027=7010=7

From the table B.4 of appendix B in the textbook, critical value corresponding to df=2,12 is 3.88.

Since, F-ratio is greater than the critical value; therefore, the null hypothesis is rejected and conclude that there are significant mean differences between the treatments.

Conclusion:

On increasing the sample size, the size of F-ratio increases. There are significant mean differences between the treatments.

b.

Expert Solution
Check Mark
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.

Answer to Problem 22P

On increasing the sample size: the effect size η2 for the study increases. The effect size η2 for the study is 0.341.

Explanation of Solution

Calculation:

The formula for η2 is

η2=SSbetweenSStotal

On increasing the sample size, the sum of squares between treatments increases more rapidly than total sum of squares, so numerator becomes larger. Hence, the effect size η2 for the study increases.

SSwithin is calculated as:

SSwithin=SS=81+90+99=270

Sum of squares between treatments is given as:

SSbetween=T2nG2N=(10)210+(50)210+(60)210(120)230=10+250+360480=140

Total sum of squares is calculated as:

SStotal=SSwithin+SSbetween=270+140=410

The effect size for the study is given as:

η2=SSbetweenSStotal=140410=0.341

Conclusion:

On increasing the sample size: the effect size η2 for the study increases. The effect size η2 for the study is 0.341.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 12 Solutions

Essentials Of Statistics For The Behavioral Sciences

Ch. 12.4 - A research report concludes that there are...Ch. 12.5 - Under what circumstances are post hoc tests...Ch. 12.5 - Prob. 2LCCh. 12.6 - Which combination of factors is most likely to...Ch. 12.6 - If an analysis of variance is used for the...Ch. 12.6 - A researcher uses an ANOVA to evaluate the mean...Ch. 12 - Why should you use ANOVA instead of several t...Ch. 12 - What value is expected for the F-ratio, on...Ch. 12 - Describe the similarities between an F-ratio and a...Ch. 12 - Calculate SSwith, SSbetween, SSwithin for the...Ch. 12 - A researcher uses an ANOVA to compare three...Ch. 12 - A researcher reports an F-ratio with dfbetween2...Ch. 12 - A researcher reports an F -ratio with df = 3.24...Ch. 12 - The following values are from an...Ch. 12 - A researcher conducts an experiment comparing four...Ch. 12 - The following summary table presents the results...Ch. 12 - A developmental psychologist is examining the...Ch. 12 - The following data were obtained from an...Ch. 12 - The following data were obtained from an...Ch. 12 - A research study comparing three treatment...Ch. 12 - The following values are from an...Ch. 12 - A research report from an independent-measures...Ch. 12 - Several factors influence the size of the F-ratio....Ch. 12 - A researcher used ANOVA and computed F = 4.25 for...Ch. 12 - The following Data were obtained from an...Ch. 12 - For the preceding problem you should find that...Ch. 12 - The following data summarize the results from an...Ch. 12 - To create the following data we started with the...Ch. 12 - An ANOVA produces an F-ratio with df 1.34. Could...Ch. 12 - The following scores are from an independent...
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License