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

2. Overview 1.Most experimental research involves two or more groups

3. When to Use an Independent t-Test 1. Two samples 2. Interval or ratio level dependent variable Either Experimental and control group comparison Or Comparing two separate independent groups (no overlap)

4. Characteristics of an Independent t- Test 1. Population means are assumed (hypothesized) to be identical 1. Treatment has no effect

5. Example of an Independent t-Test A psychologist wants to determine whether diversity training has an effect on the number of complaints filed against employees. He/she randomly assigns 20 employees to a training group, and 20 employees to a control group.

6. Example of an Independent t-Test -- continued 1. Number of Groups: 2 2. Nature of Groups: independent 3.  Known: no 4. Independent Variable: training

7. Example of an Independent t-Test -- continued 5.Dependent Variable and its Level of Measurement: complaints--interval 6.Target Population: employees 7.Appropriate Inferential Statistical Technique: t-test 8.One or two-tailed? Probably one tail

8. Example of an Independent t-Test -- continued 8. Null Hypothesis: 1. Mean of exp group – mean of control group = 0 9. Alternative Hypothesis: 1.  E -  C  0 10. Decision Rule: 1. If the p-value of the obtained test statistic is less than.05, reject the null hypothesis

9. Example of an Independent t-Test -- continued 11. Obtained Test Statistic: t 12. Decision: accept or reject null hypothesis Null—training did not affect complaints Alternative, one tail—training reduced complaints as compared to a control group without training See p. 725

10. Results Section The results of the Independent t-Test using diversity training as the independent variable and number of complaints filed against employees were statistically significant, t (18) = 2.35, p <.05. D.f. degrees of freedom = n(group 1)+n(group 2) - 2

11. Discussion Section It appears that employees undergoing diversity training have fewer complaints filed against them.

12. Assumptions of an Independent t- Test 1. Independent observations

13. SPSS Independent-Samples t- Test Procedure Analyze, Compare Means, Independent- Samples t-Test Move DV over to Test Variables Move IV over to Grouping Variable Enter numerical values of the IV under Define Groups

14. SPSS Independent-Samples t-Test Sample Printout T-Test

15. SPSS Independent-Samples t- Test Printout Group Statistics DV Levels of IV N: Sample size Mean Standard Deviation Standard Error of the Mean

16. SPSS Independent-Samples t- Test Printout -- continued Levene’s Test for Equality of Variances Test for homogeneity of variance assumption t-Test for Equality of Means If Levene test is not significant Equal variances assumed If Levene test is significant Equal variances not assumed

17. SPSS Independent-Samples t- Test Printout -- continued t-Test for Equality of Means t: obtained test statistic df: degrees of freedom Sig: p-value Divide by 2 to get one-tailed p-value Mean Difference Difference between the two sample means

18. SPSS Independent-Samples t- Test Printout -- continued Standard Error of the Difference 95% Confidence Interval of the Difference Lower Upper