1. Sampling & Estimation

2. Normal Distribution

3. Normal Sample

4. Binomial Distribution

5. Estimation

7. Sampling

8. Sampling of the Mean

9. The more observations the better! Surprice!!!!!

10. Sampling of the Variance

11. Sampling of the proportion

12. How accurate are these estimates? Can we use that to report the uncertainty in a clever way?

13. Rule of A random variable is very seldom more than two standard deviations away from the expected value.

14. … Ehh, we don’t know that one!

15. Confidence Interval for the Mean when the variance is not know

16. Confidence intervals for the variance It looks like …..

17. A 95% approximate interval for a proportion Assume normality BUT WHAT IF THIS INTERVAL CONTAINS 0 OR 1? This would be possible if n is small, if p is nearly zero or if p is nearly one.

18. Log-Transformation Believe me! Assume normality Use the expontial transformation, and write But what if the interval contains one? This could happen if n is relatively small and p is nearly one.

19. Logit-transformation and it also looks like log(1-p), for p approx one. Looks like the log-transformation, for p small To go the other way

20. The function logit(p)The function expit(p)

21. Logit-transformation Assume normality To get a 95% CI for p, we use the expit-transformation Now we are happy!

22. Why didn’t I just tell you about the logit- transformation in the first place? Because, when comparing proportions (risks), you may consider To get 95% CI here, you’ll need all three approaches.

23. How to calculate CI’s in SPSS It is easy (sort of) in the case of normally distributed variables More or less impossible in case of binomial (Use Excel)

24. Assume we have a dataset with a variable called: Alcohol Hmmmm

25. Choose Analyze General Linear Model Univariate Choose Analyze General Linear Model Univariate

26. Drag the variable Alcohol into Dependent Variable Click Options Choose Parameter estimates Drag the variable Alcohol into Dependent Variable Click Options Choose Parameter estimates

27. … And now we get