1. Two Sample Problems Lecture 4

2. Examples of various hypotheses Average salary in Copenhagen is larger than in Bælum H 0 : μ C ≥ μ B. H A : μ C < μ B. Sodium content in Furresøen is equal to the content in Madamsø H 0 : μ F = μ M. H A : μ F ≠ μ M. Proportion of Turks in Århus is the same as in Aalborg H 0 : p Å = p A. H A : p Å ≠ p A. Average height of men in Sweden is the same as in Denmark H 0 : μ S = μ D. H A : μ S ≠ μ D. The average temperature is increasing over time H 0 : μ time 1 ≥ μ time 2. H A : μ time 1 < μ time 2 if time 1 ≥ time 2.

3. Today’s tests Compare means 1.Independent samples (also called two samples in the book). 2.Paired samples. Compare variances for independent samples. Compare proportions.

4. An example An embarasing Measurement

5. Embarasing Measurement It seems to be bigger after than before!!!

6. NICE AND NORMAL !!!

7. 95% CI for mean before and after 95% CI for mean before and after The observations in living color The observations in living color

8. Another look at the data All the differences are bigger than zero

9. Look at the differences

10. How about testing if the mean difference is significantly bigger than zero?

11. Result of One Sample T-test on Differences Mean bigger than 2 SE Mean actually 6.113 SE, therefore p = 0.000

12. Equivalently The Compare Means menu is sufficient for alot of different tests

14. Blah blah – we want to see a TEST!

15. Mean difference 95% CI for difference P-value Test statistic Output

16. Conclusion If you want to test the difference between BEFORE and AFTER (or similar designs) Test if the DIFFERENCE is zero! And do this with a PAIRED T-TEST!!

17. Two-Sample T-test (unpaired) Data normal ? Equal variances? Data normal ? Equal variances?

18. Time Categorical variable Time Categorical variable Age e.g. Age > 40 Age e.g. Age > 40

19. Two-Sample Output Equal variances P-value for equal means 95% CI

20. K-Sample Data normal (in each group) ? Equal variances? Data normal (in each group) ? Equal variances?

21. If NOT!!!

22. K-Sample Output P-value

23. A Small Trick (Post Hoc)

24. OK OK, I’ll use another data set

25. RECIPE Formulate the hypothesis Formulate the model Recognize the design Check the assumptions Run the SPSS procedure Equal means or mean = some value Equal means or mean = some value Normal, binomial ect. Paired, unpaired, more groups Normal ? Equal variances? Get your p-value