## Power Analysis

### Uses

**retrospective**: to judge what the present analysis
died of
**prospective**: to provide a basis for decisions on experimental
design of a planned study by suggesting for example the minimum
sample size necessary for driving down the error variance sufficiently
so a given efect size may be picked up statistically at a given
a (i.e., least significant number)

### How this is done

When drawing conclusions from the results of a statistical
analysis we can commit one of two **errors**:

**Alpha error**: false positive, reject H_{o}
when you should not reject it
**Beta error**: false negative, fail to reject H_{o}
when you actual should reject it

**Power analysis** provides a quantitative method to estimate
the probability of obtaining a significant results in a given
situation (i.e., rejecting the null hypothesis when the alternative
hypothesis is actually true). Power analysis thus allows you to
judge how likely it is that you will detect a treatment effect
that really exists. In summary, power measures the probability
of replicating your statistical decision given a repeated use
of the same experimental design and sampling procedure. **Power**
is affected by:

**Level of Significance (a**):
changing a is not a useful choice
for fending off low power. By changing a
you are not making better decisions, you are just substituting
one error (a) for the other (b).
**Raw Effect Size (d)**: Predicting
true effect size is not trivial. You may use a combination of
approaches, including empirical data from the related literature,
pilot data, or a general consideration of the smallest effects
that you would regard as biologically meaningful in your scenario.
Within an ANOVA setting you can obtain an estimate for d as the square root of your model SS divided
by total sample size (i.e., SQRT [SS_{M} / N] )
**Standard Deviation of the Residuals (s)**:
The power of your analysis increases as the error variance decreases.
Towards that goal you can reduce treatment variability or control
for confounding factors. Obtain an estimate for s
in an ANOVA setting as the square root of the error variance
(MS error).
**Sample Size (N)**: Standard deviation of the random
error decreases with increasing sample size.

**Links:**

last modified: 3/26/14