1.
Complete the F table.
1.
Answer to Problem 23CAP
The complete F table is,
Source of Variation | SS | df | MS | |
Between groups | 48 | 3 | 16 | 7.21 |
Within groups (error) | 80 | 36 | 2.22 | |
Total | 128 | 39 |
Explanation of Solution
Calculation:
From the given data, there are four groups like unemployed, retired, part-time and full-time employees. That is,
The formulas for computing the F table are,
Source of Variation | SS | df | MS | |
Between groups | ||||
Within groups (error) | ||||
Total | 80 |
The degrees of freedom for between groups is,
The total degrees of freedom is,
The sum of squares for between groups is,
The sum of squares for error is,
The mean sum of squares for error is,
The F statistic is,
The final ANOVA table is,
Source of Variation | SS | df | MS | |
Between groups | 48 | 3 | 16 | 7.21 |
Within groups (error) | 80 | 36 | 2.22 | |
Total | 128 | 39 |
2.
Find the value of omega-squared
2.
Answer to Problem 23CAP
The value of omega-squared
Explanation of Solution
Calculation:
The given data suggests that the value of
Omega-squared
Omega-squared
Formula is given by,
Where,
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 0.06, then the effect size is medium.
- If the eta-squared value is greater than 0.14, then the effect size is larger.
The ANOVA table suggests that the value of
The omega-squared
Justification: The value of omega-squared is 0.32, which is greater than 0.14. Hence, the effect size is larger.
Hence, the value of omega-squared
3.
Observe whether the decision is to retain or reject the null hypothesis.
3.
Answer to Problem 23CAP
The decision is rejecting the null hypothesis.
Explanation of Solution
Calculation:
The given information suggests that the degrees of freedom for between groups is 3 and the degrees of freedom for error is 36
Rejection Rule:
If the value of the test statistic is greater than the critical value then reject the null hypothesis.
Critical value:
The assumed significance level is
The numerator degrees of freedom is 3, the denominator degrees of freedom as 36 and the alpha level is 0.05.
From the Appendix C: Table C.3 the F Distribution:
- Locate the value 3 in the numerator degrees of freedom row.
- Locate the value 36 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 3, the denominator degrees of freedom 36 with level of significance 0.05 is 2.86.
Thus, the critical value for the numerator degrees of freedom 3, the denominator degrees of freedom 36 with level of significance 0.05 is 2.86.
The ANOVA gives that the test statistic value is
Conclusion:
The value of test statistic is 7.21.
The critical value is 2.86.
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.
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Chapter 12 Solutions
Statistics for the Behavioral Sciences
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