(a)
Find the Chi-square test for independence at 0.05 significance level.
Check whether to retain or reject the null hypothesis test by using the chi-square test for independence.
(a)
Answer to Problem 21CAP
The value of test statistic is 6.482.
The decision is to reject the null hypothesis.
The cravings for cocaine and relapse are related.
Explanation of Solution
Calculation:
The given information is that, a study was conducted by the tests of cravings for
cocaine and relapse. The summarized table is,
Relapse | Totals | |||
Yes | No | |||
Craving | Yes | 20 | 10 | 30 |
No | 8 | 17 | 25 | |
Totals | 28 | 27 |
Table 1
The formula for total participants is,
In the formula,
The formula for expected frequency is,
In the formula, N denotes the total participants.
Test statistic:
The formula for chi-square test statistic is,
In the formula,
The formula for degrees of freedom for chi-square independence test is,
In the formula,
Null hypothesis:
Alternative hypothesis:
Expected frequency:
Substitute the corresponding values of roe totals, column totals and total frequencies for each level of categorical variable in the expected frequency formula.
Expected frequency | Relapse | Totals | ||
Yes | No | |||
Craving | Yes | 30 | ||
No | 25 | |||
Totals | 28 | 27 |
Table 2
Substitute,
Critical value:
The given significance level is
From the Appendix B: Table B.7 Critical values for Chi-square:
- Locate the value 1 in the degrees of freedom (df) column.
- Locate the 0.05 in level of significance row.
- The intersecting value that corresponds to the 1 with level of significance 0.05 is 3.84.
The critical value for
Test statistic value:
Substitute the corresponding values of observed and expected frequencies for each level of categorical variable in the test statistic formula.
Hence, the value of test statistic is 6.482.
Conclusion:
The test statistic value is 6.482.
The critical value is 3.84.
The test statistic value is greater than the critical value.
The null hypothesis is rejected.
The cravings for cocaine and relapse are related.
(b)
Find the effect size using
Find the effect size using Cramer’s V.
(b)
Answer to Problem 21CAP
The effect size using
The effect size using Cramer’s V is 0.34.
Explanation of Solution
Calculation:
The test statistic is 6.482, and value of N is 55.
The formula for Phi coefficient is,
In the formula,
The formula for effect size using Cramer’s V is,
In the formula,
Substitute,
Hence, effect size using
For
The smaller degrees of freedom are 1.
Substitute,
Hence, effect size using Cramer’s V is 0.34.
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Chapter 17 Solutions
Statistics for the Behavioral Sciences
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