Two-Sample T-Test, Independent SPSS Guide: Independent t-test A clinical psychologist wonders if eating disorders are exacerbated (i.e., worsened) by peer pressures in college sororities He compares the body weights of women within a sorority (105, 115, 90, 120, 125) to those not in a sorority (140,135,120,130,110) Is there a significant difference? Why a Independent t-test? We have (1) two groups of participants, (2) no population information, and (3) the two subjects in the two groups are not matched DATA VIEW ** VARIABLE VIEW With an independent t-test, the first column indicates the group (1=sorority, 2=other) whereas the second gives the actual data points (weight) In the VARIABLE VIEW we click on the Values column to label “1” and “2” appropriately This makes the output easier to read Go to the Analyze Menu, select Compare Means, then choose Independent samples t-test Put the variable the defines the two groups in the Grouping Variable box (e.g., group) and put the variable the contains the actual data points or scores in the Test Variable box (e.g., weight) Click on Define Groups, then specify two groups you want to compare Typically you’ll just be comparing groups and Jeff Sinn, Winthrop University, SPSS Guide - Independent T-test (rev 9/06) Two-Sample T-Test, Independent Statistical Hypotheses H 0: 1– HA: 1– Formula t obtained = = This guess says any difference is just due to sample error This guess says there is a reliable difference – a treatment effect (e.g., if you kept measuring, you’d see that the two groups don’t weigh the same) Difference observed Definitions (x1 − x ) − (µ1 − µ ) = 111 − 127 = −1.947 sˆ x1 − x2 x1 = sample mean of the first group x2 = sample mean of the second group 8.216 µ1 − µ2 = diff between population means (always 0) sˆx1 − x2 = standard error of the difference Difference expected t critical = ± 2.306 (from t-test table) −−−−−−−−−−−−−−−−−−−−−−−−−−−−− N = number of subjects in a sample [df = n1+n2 -2 = 8, two-tailed, =.05)] Mean = x (or M) (sample mean) Std Deviation = ˆsx (standard deviation as an estimate.) Std Error Mean = sˆx (standard error of the mean as an est.) SPSS Output -df = degrees of freedom = n1 + n - Group Statistics weight group sorority other N 5 Mean 111.00 127.00 Std Deviation 13.874 12.042 Std Error Mean 6.205 5.385 Sig = p obt = chance diff due to sampling error Mean Diff = x1 − x2 Std Error Diff = sˆx1 − x −−−−−−−−−−−−−−−−−−−−−−−−−−−−− d = effect size, a measure of practical signif Independent Samples Test Difference observed Test for Eq of Var t-test for Equality of Means Difference expected weight Eq Uneq F 094 Sig .767 t -1.947 -1.947 df 7.8 Sig 2-tail 087 088 Mean Diff -16.000 -16.000 sˆ = sˆ x1 − x * d = n = 216 * = 18 3715 x1 − x 111 − 127 = = 8709 ˆs 18 3715 Summary of Statistic: Retain Ho t(8) = -1.947, n.s 95% Conf Int Lower Upper -34.95 2.946 -35.01 3.011 Pobt is not below 05 so RETAIN the Ho hypothesis Always use the first line Practical Significance Std Error Diff 8.216 8.216 Note: Not required!!!! Provided only so you can see calculation method Because we did not find statistical significance, we need no calculation of practical significance Note you must first calculate before calculating d Note “n” is for just one group This says that the t-test with degrees of freedom was not significant – we must retain the Ho hypothesis We must retain the possibilities that the difference between the two groups is zero Explanation of Study Outcome: The (research) hypothesis was not supported The average weight of sorority women (M = 111) did not differ significantly from that of other women (M = 127), t(8) = -1.947, n.s Guide to write-ups: State whether the research hypothesis was supported Summarize the statistical test Summarize the practical significance (if appropriate) Jeff Sinn, Winthrop University, SPSS Guide - Independent T-test (rev 9/06) ...Two-Sample T-Test, Independent Statistical Hypotheses H 0: 1– HA: 1– Formula t obtained = = This guess says any... −−−−−−−−−−−−−−−−−−−−−−−−−−−−− d = effect size, a measure of practical signif Independent Samples Test Difference observed Test for Eq of Var t-test for Equality of Means Difference expected weight Eq Uneq... the practical significance (if appropriate) Jeff Sinn, Winthrop University, SPSS Guide - Independent T-test (rev 9/06)