2. Tables and Non Parametric Tests Lecture 5

3. Compare Means Menu

4. Compare Means Output ”Service package” ”Important package”

6. Non-normal Data Log-normal data Transform Data Compare the means of the transformed (normal) data Binomial data Really non-normal data

7. Binomial Data Are the proportions of Turks in Aalborg and Århus the same? Non- Turks Turks Aalborg46535 Århus35842

8. Are the proportions significantly different? Non- Turks Turks Aalborg46535 Århus35842 7.0% 10.5% Compare 3.5% (= 10.5 – 7.0%) with suitable SE. Compare 3.5% (= 10.5 – 7.0%) with suitable SE.

9. Another Approach Non- Turks Turks Aalborg46535 Århus35842 Non- Turks Turks Aalborg45743 Århus36634 Observed Expected In total 77 turks in a 900 sample, i.e. 8.6% In total 77 turks in a 900 sample, i.e. 8.6% We expect 34 turks in Århus (8.6% of 400) We expect 34 turks in Århus (8.6% of 400)

10. Same proportion in Aalborg and Århus? Non- Turks Turks Aalborg46535 Århus35842 Non- Turks Turks Aalborg45743 Århus36634 Observed Expected Observed and expected should be close

11. How to do it in SPSS …or data could be organized in 900 rows

12. Cross-Tabs

13. Tricks

14. Output Expected values Proportions P-value Test Statistic

15. Binomial One-Sample Two-Sample K-Sample Is proportion equal to 10% Proportions in Aalborg and Århus are equal Proportions in Aalborg, Randers, Vester Hjermislev and Århus are equal Cross-Tabs handles two or more cities (categories) 1.Calculate proportion and 95% CI 2.Is 10% in the CI? 1.Calculate proportion and 95% CI 2.Is 10% in the CI? …or use SPSS as I will show later

16. Non-Normal Data Observations Ranks

17. Statistics on Ranks Rank 14 26 37 510 812 913 1116 1417 1519 1820 Mean Ranks should be close if the two distributions are located similarly 8.6 12.4

18. How to do it in SPSS

20. Output Mann-Whitney Test ”Service package” ”Interesting package” ”Important package”

21. One-Sample (Symmetry or Location) Kiama Blowhole Data Highly skew distribution Average approx 40 sec Rarely above 100 sec Median equal to 40 sec? Only above 100 sec in 1% of the eruptions? Normal distributed ?

23. Output Data are Not Normal Not Uniform But QQ-plots are better!!

24. Location of median Median equal to 40 sec? Only above 100 sec in 1% of the eruptions?

25. Median equal to 40 sec?

26. Output NPar Tests NOPE! Median equal to 40 sec?

27. Only above 100 sec in 1% of the eruptions?

28. K samples test

29. Output Kruskal-Wallis Test ”Important package” ”Service package”

30. Overview (normal samples) One sample Two samples (paired) K samples Two samples (unpaired)

31. Overview (binomial samples) One sample Two samples (paired) K samples Two samples (unpaired)

32. Overview (non normal samples) One sample Two samples (paired) K samples Two samples (unpaired)