1. Dependent t-Test CJ 526 Statistical Analysis in Criminal Justice

2. Overview 1. Dependent Samples 1. Repeated-Measures

3. When to Use a Dependent t- Test 1. Two Dependent Samples 1. Repeated-Measures Design (before-after) 2. Matched-Subjects Design

4. Example of a Dependent t-Test  A forensic psychologist wants to determine whether physical exercise in a boot camp program has an effect on muscular strength. He/she measures the number of pull-ups 25 program participants complete at the beginning of the program (M = 3.28, SD = 1.88) and at the end of the program (M = 3.6, SD = 1.73).

5. Example of a Dependent t-Test -- continued 1. Number of Samples: 2 2. Nature of Samples: dependent (same subjects at two different points in time) 3.  Known:

6. Example of a Dependent t-Test -- continued 4. Independent Variable: participation in boot camp--exercise 5. Dependent Variable and its Level of Measurement: number of pull-ups 6. Target Population: boot camp participants

7. Example of a Dependent t-Test -- continued 7. Appropriate Inferential Statistical Technique: t test, related samples 8. Null Hypothesis: no difference between the groups before and after 9. Alternative Hypothesis: there will be a difference, boot camp participants will be able to do more pullups after training 10. Decision Rule: 1. If the p-value of the obtained test statistic is less than.05, reject the null hypothesis, one-tail test

8. Example of a Dependent t-Test -- continued 11. Obtained Test Statistic: t 12. Decision: accept or reject null hypothesis 13. D.f. = n-1 (in this case n – 1 = 25 – 1 = 24

9. Results Section  The results of the Dependent t-Test involving participating in a physical exercise program as the independent variable and number of pull-ups as the dependent variable were not statistically significant, t (24) = - 1.693.

10. Discussion Section  It appears that participating in a physical exercise program does not have an effect on developing muscular strength among participants in a boot camp program.

11. SPSS Paired-Samples t-Test Procedure  Analyze, Compare Means, Paired- Samples t-Test  Move pair of variables over to Paired Variables

12. SPSS Paired-Samples t-Test Sample Printout

13. SPSS Paired-Samples t-Test Printout  Paired Sample Statistics –Paired variables –Mean –N –Standard Deviation –Standard Error of the Mean

14. SPSS Paired-Samples t-Test Printout -- continued  Paired Samples Correlations –Paired variables –N –Correlation –Sig  p-value of correlation coefficient

15. SPSS Paired-Samples t-Test Printout -- continued  Paired Samples Test –Paired variables –Paired Differences  Mean of the Difference  Standard Deviation of the Difference  Standard Error of the Mean of the Difference  95% Confidence Interval of the Difference –Lower –Upper

16. SPSS Paired-Samples t-Test Printout -- continued  t: obtained test statistic  df: degrees of freedom  Sig: p-value –Divide by 2 to get one-tailed p-value