Independent t-Test

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

2. When to Use an Independent t-Test • Two samples • 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 • Sample means are hypothesized to be the same. Either • Treatment has no effect, comparing an experimental that received treatment and a control group that did not receive treatment • 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 • Number of Groups: 2 • Nature of Groups: independent • Independent Variable: training • Dependent variable: number of complaints

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

7. Example of an Independent t-Test -- continued 9. Null Hypothesis: • 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: • 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