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

Four critical features of experimental design Hurlbert 1984 Controls Randomization Replication Interspersion

Possible explanations? Research hypothesis (or hypotheses)

The design of a experiment Factor: humidity Variable: direction

Removing other possible effects Dealing with bias

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

Confounding factors

Independent observations

Analysis Null hypothesis: Alternative hypothesis: Probability of damp turn = 0.5

Expected frequencies for four trails dry damp drydamp drydamp drydamp drydamp drydamp drydamp drydamp drydamp drydamp drydamp drydamp drydamp drydamp

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= Calculate the probability of the other possible outcomes under the null hypothesis

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= four times = 0.25 Calculate the probability of the other possible outcomes under the null hypothesis

Binomial distribution (4 trials) Under the null hypothesis

Distribution under the null hypothesis (17 trials)

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

Binomial distribution Rejection region = 2.45% = 2.45% likelyunlikely

Why we start with the null hypothesis?

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

The Binomial Distribution Overview 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 n!n! X!(n – X)!  p X  q n – X P(X) = n!n! X!(n – X)!