Experimental design

1. Experimental design Based on Chapter 2 of D. Heath (1995). An Introduction to Experimental Design and Statistics for Biology. CRC Press.

2. Four critical features of experimental designHurlbert 1984 • Controls • Randomization • Replication • Interspersion

4. Possible explanations?Research hypothesis (or hypotheses)

5. The design of a experiment • Factor: humidity • Variable: direction

8. Removing other possible effects • Dealing with bias

11. Other design issues • Number of woodlice • Which woodlice • They must be representative of the population of reference

12. Confounding factors

13. Independent observations

14. Probability of damp turn = 0.5 Analysis • Null hypothesis: • Alternative hypothesis: Probability of damp turn = 0.5

15. damp dry dry damp dry damp dry dry dry dry damp damp damp damp dry dry dry dry damp damp damp damp dry dry dry dry damp damp damp damp Expected frequencies for four trails

16. Example • Damp*Damp*Damp*Damp • If order does not matter there is only one way to obtain four damp turns and the combined probability (under the assumption of independence) is 0.5*0.5*0.5*0.5= 0.0625 • Calculate the probability of the other possible outcomes under the null hypothesis

17. Exercise • There are four ways to obtain three damp turns: Damp*Damp*Damp*Dry Damp*Damp*Dry*Damp Damp*Dry*Damp*Damp Dry*Damp*Damp*Damp • and the combined probability (under the assumption of independence) is 0.5*0.5*0.5*0.5= 0.0625 four times = 0.25 • Calculate the probability of the other possible outcomes under the null hypothesis

18. Binomial distribution (4 trials)Under the null hypothesis

19. Distribution under the null hypothesis(17 trials)

20. What do you conclude if we observed 14 damp turns out of 17 ?

21. Binomial distribution Rejection region Rejection region unlikely likely unlikely 0.0000+0.0001+0.0010+0.0052+0.0182= 2.45% 0.0182+0.0052+0.0010+0.0001+0.0000= 2.45%

22. Why we start with the null hypothesis?

23. The main points • Use a mathematical model to produce a sampling distribution of all possible values of the test statistic assuming that the null hypothesis is true • Find the probability associated with a a particular value occurring in a particular experiment • Use the probability to make a decision about whether a particular result is likely or unlikely

24. n! n! X!(n – X)! X!(n – X)! The Binomial DistributionOverview • However, if order is not important, then where is the number of ways to obtain X successes in n trials, and n! = n (n – 1)  (n – 2)  …  2  1 P(X) = pX qn – X