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

2. 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)

3. Characteristics of an Independent t- Test 1. Sample means are hypothesized to be the same. Either 1. Treatment has no effect, comparing an experimental that received treatment and a control group that did not receive treatment 2. Or, two independent groups are the same with respect to a DV

4. 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.

5. Example of an Independent t-Test -- continued 1. Number of Groups: 2 2. Nature of Groups: independent 3. Independent Variable: training 4. Dependent variable: number of complaints

6. 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

7. Example of an Independent t-Test -- continued 9. Null Hypothesis: 1. Mean of exp group – mean of control group = 0 10. Alternative Hypothesis: Mean of experimental group minus mean of control group does not equal 0 11. Decision Rule: 1. If the p-value of the obtained test statistic is less than.05, reject the null hypothesis

8. Example of an Independent t-Test -- continued 12. Obtained Test Statistic: t 13. Decision: accept or reject null hypothesis Null hypothesis—training did not affect complaints, comparing experimental and control groups Alternative, one tail—training reduced complaints as compared to a control group without training See p. 725

9. 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

10. Discussion Section It appears that employees undergoing diversity training have fewer complaints filed against them. Or, if the null hypothesis was retained, the conclusion would be that diversity training did not affect the number of complaints filed

11. 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

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

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

14. 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

15. 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

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