2. Tables and Non Parametric Tests Lecture 5

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

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

5. 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.

6. 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)

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

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

9. Cross-Tabs

10. Tricks

11. Output Expected values Proportions P-value Test Statistic

12. 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

13. 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 ?

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

15. Median equal to 40 sec?

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

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