1. Statistical Power

2. Ho : Treatments A and B the same
HA: Treatments A and B different

3. Critical value at alpha=0.05
Points on this side, only 5% chance from distribution A.
Frequency A
Area = 5%
A could be control treatment
B could be manipulated treatment

4. If null hypothesis true, A and B are identical
Probability that any value of B is significantly different than A = 5% A B
Probability that any value of B will be not significantly different from A = 95%

5. What you say:
Decide NOT significantly different (do not reject Ho)
Decide significantly different (reject Ho)
Ho true (same)
Type 1 error
Ho false (different)
Type 2 error
Reality

6. If null hypothesis true, A and B are identical
Probability that any value of B is significantly different than A = 5% = likelihood of type 1 error A B
Probability that any value of B will be not significantly different from A = 95%

7. If null hypothesis false, two distributions are different
Probability that any value of B is significantly different than A = 1- beta = power A B
Probability that any value of B will be not significantly different from A = beta = likelihood of type 2 error

8. Effect size = difference in means SDB
Effect size = difference in means SD

9. 1. Power increases as effect size increasesB
Beta = likelihood of type 2 error

10. 2. Power increases as alpha increasesB
Beta = likelihood of type 2 error

11. 3. Power increases as sample size increases
Low n A B

12. 3. Power increases as sample size increases
High n A B

13. Effect size
Alpha
Power
Sample size

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.

15. Example : Fox hunting in the UK
(posteriori)

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 Nature 419: 34
Aebischer et al Nature 423: 400

17. 157 plots where the fox population monitored.
Alpha = 0.05
Effect size if hunting affected fox populations: 13%

18. 157 plots where the fox population monitored.
Alpha = 0.05
Effect size if hunting affected fox populations: 13%
Power = 0.95 !

19. Class exercise:
Means and SD of parasite load (p>0.05):
Daphnia magna 5.9 ± 2 (n = 3)
Daphnia pulex ± 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?

20. Good options for increasing sample size:
More replicates
More blocks
False options for increasing sample size:
More “repeated measurements”
Pseudoreplication