POWER CALCULATIONS David Gardner School of Veterinary Medicine University of Nottingham

POWER CALCULATIONS What are they? Why do them? Examples

POWER CALCULATIONS What are they? Why so them? Examples

POWER CALCULATIONS Conventional power analysis addresses the question: for a given null hypothesis (H0) or alternative hypothesis (H1) and at a given sample size and variation... ...what is the probability of rejecting H0 when H1 is actually true (and H0 is false). This probability is called statistical power. The inverse i.e. (1 – power) = gives the related quantity, b, the probability of rejecting H0 when H0 is true (and H1 is false)..i.e. Type II error.

Factors influencing POWER Sample size Power increases as sample size increases

Factors influencing POWER Effect size A hypothesis test has greater chance of detecting real difference if effect is large rather than small, therefore can have less n

Factors influencing POWER Increasing sample size..... Variability More power with less variation, less power with highly variable responses Figure 18.1 in ‘at a glance’

Sample size...considerations If study n is small we may have inadequate power to detect an important effect, therefore nothing seen – was this due to low n or that there was actually nothing going on...was the whole study a waste of time... ...on the other hand. A large study is time-consuming, expensive, unethical (loads of patients/animals etc...).... A balance has to be struck... how many patients/samples to give best chance of seeing something if that something is genuinely there...?

Sample size...need to know So how do? if number of tests (always the case) then focus on most important or do a range and choose largest sample size. Need to; Specify power of test (usually 80% as minimum) Choose significance level (usually 5%, or if want to be really sure as outcome is critical then choose 1%) Know variability, the std deviation and its square, the variance or RMS (residual mean square) An estimate of effect size (i.e. What difference between means would be considered important)

Sample size...need to know So how do? Power, easy to do Significance level, easy to do Variability, do dummy test, pilot study, use other peoples data An estimate of effect size, as in 3. What would be considered important in your opinion and in other peoples opinion

Sample size...your go! Try doing a sample size calc on the data given...... Prospective on data, i.e. How many subjects need for next study.... 2) Retrospective study, i.e. Were conclusions valid?

Retrospective example...leptin 2 groups T-test C vs. Obese N=6/group gender Effect size 2.3 – 1.3 = 1.0 SEM = 0.3,0.5 Variance = 1.5/0.5 10 df Power ? 40-50% N=12 per group