1. Independent t-tests

2.  Use when:  You are examining differences between groups  Each participant is tested once  Comparing two groups only

3. Mean Group 1 - Mean Group 2 ___________________________________ Spread of the groups' data points  t is larger (more likely significant) when: ◦ Two groups’ means are very different ◦ When spread (variance) is very small

4.  Observations are independent  Samples are normally distributed  Samples should have equal variance ◦ There is a “fix” for violations of this assumption that will be discussed in lab

5. t = X 1 – X 2 (n 1 -1) s 1 2 + (n 2 – 1)s 2 2 n 1 +n 2 n 1 + n 2 - 2 n 1 n 2 X 1 = mean for group 1 X 2 = mean for group 2 n 1 = number of participants in group 1 n 2 = number of participants in group 2 s 1 2 = variance for group 1 s 2 2 = variance for group 2

6.  Study: ◦ Effects of GRE prep classes on test scores ◦ One group given prep classes  (1400, 1450, 1200, 1350, 1300) ◦ One group given no classes  (1400, 1200, 1050, 1100, 1200)

7.  1. State hypotheses ◦ Null hypothesis: there is no difference between test scores in the groups with or without prep classes  μ prep = μ noprep ◦ Research hypothesis: there is a difference in test scores between the groups with and without prep classes  X prep ≠ X noprep

8. t = X 1 – X 2 (n 1 -1) s 1 2 + (n 2 – 1)s 2 2 n 1 +n 2 n 1 + n 2 - 2 n 1 n 2 X 1 = mean for group 1 X 2 = mean for group 2 n 1 = number of participants in group 1 n 2 = number of participants in group 2 s 1 2 = variance for group 1 s 2 2 = variance for group 2

9. X 1 – X 2  Prep group: 1400, 1450, 1200, 1350, 1300  Noprep group: 1400,1200, 1050, 1100, 1200

10.  Degrees of freedom ( df ): Describes number of scores in sample that are free to vary (without changing value of descriptive statistic).  Needed to identify the critical value  df = (n 1 - 1) + (n 2 – 1) (for t-test only)

11.  **if dfs are bigger than biggest value in chart, use infinity row  **if precise dfs are not listed, use the next smallest to be conservative

12.  6. Determine whether the statistic exceeds the critical value ◦ 2.03 < 2.31 ◦ So it does not exceed the critical value ◦ THE NULL IS REJECTED IF OUR STATISTIC IS BIGGER THAN THE CRITICAL VALUE – THAT MEANS THE DIFFERENCE IS SIGNIFICANT AT p <.05!!  7. If not over the critical value, fail to reject the null  & conclude that there was no effect of GRE training on test scores

13.  In results ◦ There was no significant difference in test scores between participants given the GRE prep course (M = 1340, SD = 96.18) and those given no GRE prep course (M = 1190, SD = 134.16), t(8) = 2.03, n.s.  If it had been significant: ◦ Participants given the GRE prep course had significantly higher test scores (M = 1340, SD = 96.18) than those given no GRE prep course (M = 1190, SD = 134.16), t(8) = 2.80, p <.05.

14.  Whether the effect/difference was significant or not  The outcome in the study  The different groups or categories being compared in the study  The mean and SD for each group or category  The t statistic and p-value, as shown in examples

15.  Remember: Just because means are different, it does not mean they are meaningfully different  Need to examine significance ◦ i.e., likelihood that the differences are due to chance

16.  A measure of the magnitude of the difference between groups ES = X 1 – X 2 SD