S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 9: t test

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This week what is t test and when to use TTEST function T-test ToolPak

Example Eating attitudes test on a group of 297 Australian and a group of 249 Indian university students. Each group is only tested once. Sjostedt, J. P.; Shumaker, J. F. & Nathawat, S. S. (1998). Eating disorders among Indian and Australian university students. Journal of Social Psychology, 138(3), Which statistic approach we will use?

T test assumption The amount of variability in each of the two groups is equal

T test formula : is the mean for Group 1 : is the mean for Group 2 : is the number of participants in Group 1 : is the number of participants in Group 2 : is the variance for Group 1 : is the variance for Group 2

T test steps Group 1 Group

T test steps Step 1: A statement of the null and research hypotheses. Null hypothesis: there is no difference between two groups Research hypothesis: there is a difference between the two groups

T test steps Step 2: setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis 0.05 It is up to your decision

T test steps Step 3: Selection of the appropriate test statistic Using Figure 9.1 to determine which test statistic is good for your research T test

T test steps Step 4: computation of the test statistic value Calculate mean and standard deviation T calculation t=

T test steps Step 5: determination of the value needed for the rejection of the null hypothesis Table B2 in Appendix B (S-p360) Degrees of freedom (df): approximates the sample size Group 1 sample size -1 + group 2 sample size -1 Our test df= 58 Two-tailed or one-tailed Directed research hypothesis  one-tailed Non-directed research hypothesis  two-tailed Choose the df close to your sample size According to Table B2, df=58, two-tailed, Type I error=0.05,  the value needed to reject the null hypothesis with 58 degrees of freedom at the 0.05 level of significance is

T test steps Step 6: A comparison of the obtained value and the critical value and If the obtained value > the critical value, reject the null hypothesis If the obtained value < the critical value, accept the null hypothesis

T test steps Step 7 and 8: make a decision What is your decision and why?

Interpretation t (58) = -.14, p>0.05 Write down your interpretation and discuss with your group

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

Excel: TTEST function It does not compute the t value It returns the likelihood that the resulting t value is due to chance (the possibility of the difference of two groups is due to chance) 88% of possibility that two groups are different caused by chance  without chance, 88% possibility that the two groups are not different  there is no different between these two groups

Excel ToolPak Group 1 Group

Excel ToolPak Select t-test: two sample assuming equal variances t-Test: Two-Sample Assuming Equal Variances Variable 1Variable 2 Mean Variance Observations30 Pooled Variance Hypothesized Mean Difference0 df58 t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail

Effect size If two groups are different, how to measure the difference among them Effect size ES: effect size : the mean for Group 1 : the mean for Group 2 SD: the standard deviation from either group

Effect size A small effect size ranges from 0.0 ~ 0.2 Both groups tend to be very similar and overlap a lot A medium effect size ranges from 0.2 ~ 0.5 The two groups are different A large effect size is any value above 0.50 The two groups are quite different ES=0  the two groups have no difference and overlap entirely ES=1  the two groups overlap about 45%

Exercise Chapter Data set 1 1 (s-p209) 2 3 4