1. S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 10: t test

2. Last week

3. This week T test for dependent means How to compute the observed t value Interpret the t value Use TTEST and TDIST function ToolPak tool

4. T test for dependent Means that a single group of the same objects is being studied under two conditions

5. Example Three professors at University of Alabama studied the effects of resource and regular classrooms on the reading achievement of learning-disabled children. A group of children was test before they take the 1-year daily instruction and after they took the 1-year daily instruction. Which statistical test we should use?

6. T test for dependent : the sum of all the difference between groups : the sum of the differences squared between groups n : the number of pairs of observations

7. T test for dependent pretestposttestdifferenceD2 37416 5839 4624 6711 5839 594 4624 5611 374 6824 7811 871 7924 610416 7924 8911 8800 981 94-525 84-416 75-24 761 6939 7811 812416

8. T test for dependent Step1: A statement of the null and research hypotheses

9. T test for dependent Step2: setting the level of risk (or the level of significance or Type I error) associated with null hypothesis 0.05

10. T test for dependent Step3: selection of the appropriate test statistics Following Figure 10.1 T test for dependent = t test for paired samples = t test for correlated samples

11. T test for dependent Step4: computation of the test statistic value t=2.45 How to calculate

12. T test for dependent Step5: determination of the value needed for rejection of the null hypothesis Table B2 df=n-1=25-1=24 One tailed: because research hypothesis is directed

13. T test for dependent Step6: a comparison of the t value and the critical value 2.45>1.711 Reject the null hypothesis

14. T test for dependent Step7 and 8: time for a decision There is the difference between pretest and posttest

15. Excel: TTEST function TTEST (array1, array2, tails, type) array1 = the cell address for the first set of data array2 = the cell address for the second set of data tails: 1 = one-tailed, 2 = two-tailed type: 1 = a paired t test; 2 = a two-sample test (independent with equal variances); 3 = a two- sample test with unequal variances

16. Excel: TTEST function TTEST (array1, array2, tails, type) Type: Independent Two groups with no relationship  The weights of men and women with no relationship Dependent Matched, or paired samples  The weights of men and women in a relationship (one man is matched or paired with one woman based on relationship) Repeated measures  One group is pre- and post-tested

17. Excel TTEST() It does not computer the t value It returns the likelihood that the resulting t value is due to chance Less than 1% of the possibility that two tests are different due to chance  the two tests are difference due to other reasons than chance.

18. Excel ToolPak T test: paired two sample for means option t-Test: Paired Two Sample for Means pretestposttest Mean6.327.52 Variance2.9766666673.343333333 Observations25 Pearson Correlation0.050718341 Hypothesized Mean Difference0 df24 t Stat-2.449489743 P(T<=t) one-tail0.010991498 t Critical one-tail1.710882067 P(T<=t) two-tail0.021982997 t Critical two-tail2.063898547

19. Exercises S-p223