Statistics for the Behavioral Sciences
Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781452286907
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
bartleby

Videos

Question
Book Icon
Chapter 12, Problem 22CAP

(a)

To determine

Complete the F table.

(a)

Expert Solution
Check Mark

Answer to Problem 22CAP

The complete F table is,

Source of VariationSSdfMSFobt
Between groups3021511.72
Within groups (error)50391.28
Total8041

Explanation of Solution

Calculation:

From the given data, there are three groups highly experienced, moderately experienced and inexperienced athletes. The sample size is 14. That is, k=3 and n=14.

The formulas for computing the F table are,

Source of VariationSSdfMSFobt
Between groupsSSBGk1SSBGdfBGMSBGMSE
Within groups (error)SSENkSSEdfE
Total80(N1) or (kn1)

Where SSBG indicates the sum of the squares of variation between the groups, SST denotes the Total sum of squares, SSE denotes the error sum of squares, MSE indicates the means squares due to error, MSBG indicates the means squares due to variation between the groups.k indicates the levels of factor. n represents the number of participants in each groups. N represents the total number of participants.

Source of VariationSSdfMSFobt
Between groups8050=3031=2302=15151.28=11.72
Within groups (error)50423=395039=1.28
Total80(14×3)1=41

Thus, the ANOVA table is,

Source of VariationSSdfMSFobt
Between groups3021511.72
Within groups (error)50391.28
Total8041

(b)

To determine

Find the value of eta-squared (η2).

(b)

Expert Solution
Check Mark

Answer to Problem 22CAP

The value of eta-squared (η2) is 0.38 and it represents thelarge effect size.

Explanation of Solution

Calculation:

The ANOVA table suggests that the value of SSBG is 30 and the value of SST is 80.

Eta-squared (η2):

One of the measure for effect size is Eta-squared (η2). Eta-squared computed as the sum of squares between groups divided by the total sum of squares.

Formula is given by,

η2=SSBGSST.

Where, SSBG represents the sum of squares between groups and SST represents the total sum of squares.

Description of effect size using eta-squared:

  • If the eta-squared value is less than 0.01, then the effect size is small.
  • If the eta-squared value lies between 0.01 and 0.09, then the effect size is medium.
  • If the eta-squared value is greater than 0.25, then the effect size is larger.

Substitute the value of SSBG is 30 and the value of SST is 80.

The eta-squared value is,

η2=SSBGSST=3080=0.38

Justification: The value of eta-squared is 0.38, which is greater than 0.25. Hence, the effect size is larger.

Hence, the value of eta-squared (η2) is 0.38 and it represents the large effect size.

(c)

To determine

Observe whether the decision is to retain or reject the null hypothesis.

(c)

Expert Solution
Check Mark

Answer to Problem 22CAP

The decision is rejecting the null hypothesis.

Explanation of Solution

Calculation:

The given information suggest that the degrees of freedom for between groups is 2 and the degrees of freedom for error is 39.

Rejection Rule:

If the value of the test statistic is greater than the critical value then reject the null hypothesis.

The given ANOVA table suggests that the degrees of freedom for between groups is 2 and the degrees of freedom for error is 39. That is, the degrees of freedom for numerator is 2 because the between group degrees of freedom represents the numerator degrees of freedom and the degrees of freedom for denominator is 39 because the error group degrees of freedom represents the denominator degrees of freedom.

Critical value:

Assume that the significance level is α=0.05.

The numerator degrees of freedom are 2, the denominator degrees of freedom as 39 and the alpha level is 0.05.

From the Appendix B: Table B.3 the F Distribution:

  • Locate the value 2 in the numerator degrees of freedom row.
  • Locate the value 39 in the denominator degrees of freedom column.
  • Locate the 0.05 in level of significance.
  • The intersecting value that corresponds to the numerator degrees of freedom 2, the denominator degrees of freedom 39 with level of significance 0.05 is 3.24.

Thus, the critical value for the numerator degrees of freedom 2, the denominator degrees of freedom 39 with level of significance 0.05 is 3.24.

The ANOVA gives that the test statistic value is Fobt=11.72.

Conclusion:

The value of test statistic is 11.72

The critical value is 3.24.

The value of test statistic is greater than the critical value.

The test statistic value falls under critical region.

By the decision rule, the conclusion is rejecting the null hypothesis.

Hence, the decision is rejecting the null hypothesis.

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!
Students have asked these similar questions
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…
If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9.   The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24?   The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Introduction to experimental design and analysis of variance (ANOVA); Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=vSFo1MwLoxU;License: Standard YouTube License, CC-BY