2. Independent t-tests Uses a sampling distribution of differences between means 1

3. The test statistic for independent samples t-tests  Recall the general form of the test statistic for t-tests:  Recall the test statistic for the single sample t-test… Horizontal axis value = sample mean Distribution mean = mean of distribution of sample means Distribution SD = SD of distribution of sample means 1 2 3

4.  So how about the independent samples t- test? The test statistic for independent samples t-tests Horizontal axis value = ? 1

5.  So how about the independent samples t- test? The test statistic for independent samples t-tests Horizontal axis value = difference between 2 sample means 1

6.  So how about the independent samples t- test? The test statistic for independent samples t-tests Distribution mean = ? 1 2

7.  So how about the independent samples t- test? The test statistic for independent samples t-tests SD of sampling distribution = ? 1 1

8. the SD of the distribution of differences between 2 sample means  So how about the independent samples t- test? The test statistic for independent samples t-tests SD of sampling distribution = ? 1

9. On the SD of the distribution:  Look at the SD (SE M ) in more detail Where: 1

10. What affects significance?  Mean difference  With larger observed difference between two sample means, it is less likely that the observed difference in sample means is attributable to random sampling error  Sample size  With larger samples, it is less likely that the observed difference in sample means is attributable to random sampling error  Sample SD:  With reduced variability among the cases in each sample, it is less likely that the observed difference in sample means is attributable to random sampling error  See applet: http://physics.ubishops.ca/phy101/lectures/Beaver/twoSampleTTest.html 1

11. d of f for the test statistic  The d of f changes from the one- sample case  comparing two independent means becomes If the 2 groups are of equal size 1

12. Reporting t-test in text Descriptive statistics for the time to exhaustion for the two diet groups are presented in Table 1 and graphically in Figure 1. A t-test for independent samples indicated that the 44.2 (  2.9) minute time to exhaustion for the CHO group was significantly longer than the 38.9 (  3.5) minutes for the regular diet group (t 18 = - 3.68, p  0.05). This represents a 1.1% increase in time to exhaustion with the CHO supplementation diet. Should also consider whether the difference is meaningful – see effect sizes, later 1

13. Reporting t-test in table  Descriptives of time to exhaustion (in minutes) for the 2 diets. Note: * indicates significant difference, p  0.05 GroupnMeanSD Reg Diet1038.9*3.54 CHO sup1044.22.86 1

14. Reporting t-test graphically Figure 1. Mean time to exhaustion with different diets. 1

15. Reporting t-test graphically Figure 1. Mean time to exhaustion with different diets. 1

16. Summary/Assumptions of the independent t-test  Use when the assumption of no correlation between the samples is valid  Don’t test for it…just examine whether the assumption is fair  Use when the two samples have similar variation (SD)  Test for in output (see next few slides) 1 2

17. t-tests in SPSS  First note the data format: one continuous variable (in this case, age) 1

18. t-tests in SPSS  Second, run the procedure: drag the test variable over and specify μ 1

19. t-tests in SPSS  Third, check the output: N, Mean, SD, SE M significance (if α =.05, then <.05 is significant) df = n-1 = 19 1 2

20. independent-tests in SPSS  First, check the data: One grouping variable One test variable 1

21. independent-tests in SPSS  Second, run the procedure: 1

22. independent-tests in SPSS  Second, run the procedure: 1. slide variables over 2. click “define groups” 3. define groups 1 2

23. independent-tests in SPSS  Third, examine the output: N, Mean, SD, SE M test for equal variances (>.05 is good) significance (if α =.05, then <.05 is significant) 1 2 3 4