# Sample Size Calculator

## Determines the minimum number of subjects for adequate study power

### Study Group Design

Two study groups will each receive different treatments.

### Primary Endpoint

The primary endpoint is binomial - only two possible outcomes.

### Anticipated Means

Group 1 ±
Group 2 Enrollment ratio ### Anticipated Incidence

Group 1 Group 2 Enrollment ratio ### Anticipated Incidence

Known population Study group ### Anticipated Mean

Known population ±
Study group ### Type I/II Error Rate

Alpha Power Press 'Calculate' to view calculation results.

This calculator uses a number of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect.1

Before a study is conducted, investigators need to determine how many subjects should be included. By enrolling too few subjects, a study may not have enough statistical power to detect a difference (type II error). Enrolling too many patients can be unnecessarily costly or time-consuming.

Generally speaking, statistical power is determined by the following variables:

• Baseline Incidence: If an outcome occurs infrequently, many more patients are needed in order to detect a difference.
• Population Variance: The higher the variance (standard deviation), the more patients are needed to demonstrate a difference.
• Treatment Effect Size: If the difference between two treatments is small, more patients will be required to detect a difference.
• Alpha: The probability of a type-I error -- finding a difference when a difference does not exist. Most medical literature uses an alpha cut-off of 5% (0.05) -- indicating a 5% chance that a significant difference is actually due to chance and is not a true difference.
• Beta: The probability of a type-II error -- not detecting a difference when one actually exists. Beta is directly related to study power (Power = 1 - β). Most medical literature uses a beta cut-off of 20% (0.2) -- indicating a 20% chance that a significant difference is missed.

#### Post-Hoc Power Analysis

To calculate the post-hoc statistical power of an existing trial, please visit the post-hoc power analysis calculator.

1. Rosner B. Fundamentals of Biostatistics. 7th ed. Boston, MA: Brooks/Cole; 2011.

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