## Advanced Statistics - Biology 6030 |

## Bowling Green State University, Fall 2017 |

**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)

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.

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last modified: 3/26/14

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