Power and sample size

What is Statistical Significance

Statistical Significance: The p-value is the probability of obtaining the observed results, or results more extreme, assuming that the null hypothesis is true. [2] In other words, it is the probability of a Type I error

What is the Alpha Level

Alpha Level: By convention, the acceptable probability of a Type I error (alpha) is set at 0.05. [2] This means that researchers are willing to accept a 5% chance of wrongly rejecting the null hypothesis

What is Power

Power: Statistical power measures the ability of a study to detect a real effect, if one exists. [3] It is defined as the probability of not committing a Type II error (1 - beta)

What does power depend on

Power depends on the size of the effect in the population (effect size), the alpha level, and the sample size. [3] Power, effect size, alpha, and sample size are all interdependent. [3] If three of these are specified, the sample size can be calculated

What are effect sizes

Effect Sizes: Pearson's R and Cohen's d are examples of effect sizes. [4]
Many studies are underpowered because the sample size is too small to detect a small effect size. [4] This can lead to the conclusion that there is no difference between groups when there really is a difference (Type II error).

When do you calculate power

The most common time to do power calculations is during the planning stages of a study to determine the sample size. [5] However, power calculations can also be done after a study is completed if the sample size is already known (e.g., in a register-based study).

How do we use these statistics to determine type 1 and 2 errors

Alpha, Beta, and Power:
Alpha is the probability of a false positive, beta is the probability of a false negative, and power is 1 - beta. [6] Reducing the alpha threshold from 0.05 to 0.01 will reduce the chance of false positives but will also decrease power.

What reduces power

Random error (noise) will reduce power,
imprecise measurements.

When does it become difficult to further increase power

Once the control group is 4-5 times larger than the patient group

What does power equal

1- beta

What is the ideal level of power and beta

Aim for power=0.8, so beta =0.2

What does the odds ratio calculate

the association between exposure and outcome , the odds of exposure among cases(a/c) divided by the odds of exposure among controls (b/d)