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Published on : Feb 10, 2014
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Slide 1 - Statistical Power
Slide 2 - Ho : Treatments A and B the same HA: Treatments A and B different
Slide 3 - Points on this side, only 5% chance from distribution A. Area = 5% Critical value at alpha=0.05 Frequency A A could be control treatment B could be manipulated treatment
Slide 4 - A B If null hypothesis true, A and B are identical Probability that any value of B will be not significantly different from A = 95% Probability that any value of B is significantly different than A = 5%
Slide 5 - A B If null hypothesis true, A and B are identical Probability that any value of B will be not significantly different from A = 95% Probability that any value of B is significantly different than A = 5% = likelihood of type 1 error
Slide 6 - What you say: Reality
Slide 7 - A B If null hypothesis false, two distributions are different Probability that any value of B will be not significantly different from A = beta = likelihood of type 2 error Probability that any value of B is significantly different than A = 1- beta = power
Slide 8 - A B Effect size Effect size = difference in means SD
Slide 9 - A B 1. Power increases as effect size increases Beta = likelihood of type 2 error Power Effect size
Slide 10 - A B 2. Power increases as alpha increases Beta = likelihood of type 2 error Power
Slide 11 - A B 3. Power increases as sample size increases Low n
Slide 12 - A B 3. Power increases as sample size increases High n
Slide 13 - Power Effect size Alpha Sample size
Slide 14 - Types of power analysis: A priori: Useful for setting up a large experiment with some pilot data Posteriori: Useful for deciding how powerful your conclusion is (definitely? Or possibly). In manuscript writing, peer reviews, etc.
Slide 15 - Example : Fox hunting in the UK (posteriori)
Slide 16 - Hunt banned (one year only) in 2001 because of foot-and-mouth disease. Can examine whether the fox population increased in areas where it used to be hunted (in this year). Baker et al. found no effect (p=0.474, alpha=0.05, n=157), but Aebischer et al. raised questions about power. Baker et al. 2002. Nature 419: 34 Aebischer et al. 2003. Nature 423: 400
Slide 17 - 157 plots where the fox population monitored. Alpha = 0.05 Effect size if hunting affected fox populations: 13%
Slide 18 - 157 plots where the fox population monitored. Alpha = 0.05 Effect size if hunting affected fox populations: 13% Power = 0.95 !
Slide 19 - Class exercise: Means and SD of parasite load (p>0.05): Daphnia magna 5.9 ± 2 (n = 3) Daphnia pulex 4.9 ± 2 (n = 3) (1) Did the researcher have “enough” power (>0.80)? (2) Suggest a better sample size. (3) Why is n=3 rarely adequate as a sample size?
Slide 20 - How many samples? PCBs in salmon from Burrard inlet and Alaska In an initial survey (3 individuals each), we find the following information (mean, standard deviation) Burrard – 120.5 ± 75.9 ppb Alaska – 75.2 ± 71.9 ppb The two error bars overlap, but that’s still a big difference and we only took 3 samples The difference could be “hidden” the sizes of the errors This would be reduced by increased samples, but how many should we take?
Slide 21 - How many samples? Our difference between (q) is ~40, therefore if our confidence limits (SE) were <20ppb, we should have a difference between populations, Burrard – 120.5 ± 75.9 ppb Alaska – 75.2 ± 71.9 ppb How many samples do we therefore need??
Slide 22 - Re-arrange the equation… So we should take 56 samples to be reasonably sure of a significant difference
Slide 23 - Don’t get silly..