Power analysisor

What does it mean

P<0.05

And mainly what does it mean

P>0.05(According to Scheiner & Gurevitch 2001: Desing and analysis of ecological

experiments. 2nd ed. Oxford Univ. Press)

Decision table

Power = 1-β

Effect size

• Absolute effect size – after fertilization, the biomass will increase by 100 g.m-2

• Relative effect size – after fertilization, the biomass will increase by 5%

• Standardized effect size – Absolute effect size/s.d.

Power of the test depends on the effect size

At small number of replications, we have problem to demonstrate rather large effect, at large number of replications, we are able to demonstrate effect that has nearly no biologicl meaning.

Power analysis provides

• Power of the test as a function of effect size, variability of data (these to provide standardized effect size) and sample(s) size – i.e. number of replications

• Usefulness of pilot experiment to get variability and expected effect size

• Useful for experiment/sampling design planning; useful also, when the test is not significant, to see whether we even had a chance to demonstrate the effect

Example 1 – correlation coefficient

• Relationship between no of species and biomass (and I expect linear relationship)

• How many quadrat I need to get significant result?

• Factors which I need to know – Expected value of correlation coefficient in the

(statistical) „population“ (i.e. The effect size, the size of deviation from the H0)

– Required power of the test

Example 2 – t-test

• Difference in no of species between mown and unmown plots (independent samples)

• What I need to know: Expected difference, „population“ sigma – homoscedascity expected

• S.E.S.= Difference/sigma

• Required power of the test

• How many quadrats I need

Es = S.E.S. = Difference/Sigma

Possible questions• Biologically significant is increase of seed production

after competitor removal by 10% (either a number which is estimated by a rule of thumb, or based on some evolutionar model); the increase of productivity by fertilization is economical only, when it is more than 1000kg/ha.

• We assume to know variability in the data (best professional guess, or from pilot experiment)

• Sample(s) size required to demonstrate the effect (i.e. To reject H0 at 5% significance level) with probability at least 90% (power of the test, i.e. 1-β)

• Alternatively: What is/was the chance to demonstrate the effect with no. of replications available

Missleading word „significant“

• Statistical significance does not imply biological significance

• (Nearly) each null hypothesis is not correct – its rejection then depends on the number of replications we are able to get (we are often limited in this respect).

• Dangers of careless use of „computerized sampling“)

• Power analysis

I like the approach (Scheiner & Gurewith):

Vertical lines are confidence intervals (CI)

This approach can be used for estimate of sample size needed (CI size decreases with N)

Presenting CI in paper provides good indication of biíological significance.