Determine the required sample size for comparisons of means or proportions

Leave one of the inputs blank to determine its value. By default the sample size inputs (*n1* and *n2*) are left empty and the required sample size for both groups is calculated. If values are provided for both *n1* and *n2* the value for any one of the other inputs left blank will be calculated. If only a value for *n1* (*n2*) is entered, all other inputs must be provided to determine the required sample size for *n2* (*n1*)

- Sample size: Number of respondents required
- Confidence level: 1 - significance level (e.g, .95 = 1 - .05).
^{1, 2} - Power: 1 - \(\beta\) (e.g, .8 = 1 - .2).
^{3}

- Delta: Difference between group means that we hope to detect
- Std. deviation: Assumed standard deviation

- Proportion 1: Assumed proportion in group 1 (e.g., .1)
- Proportion 2: Proportion 1 plus the difference we hope to detect (e.g., .1 + .05 = .15)

**Note:** The (match) the control group sample size (*n1*) to the test group sample size (*n2*) leave both inputs for sample size blank (i.e., groups are of the same size). If a value for *n1* or *n2* is provided group sizes are likely to differ

^{1} The **significance level**, often denoted by \(\alpha\), is the highest probability you are willing to accept of rejecting the null hypothesis when it is actually true. A commonly used significance level is 0.05 (or 5%)

^{2} \(1 - \alpha\) is called the **confidence level**. A commonly used confidence level is 0.95 (or 95%)

^{3} Beta (\(\beta\)), is the probability of accepting the null hypothesis when it is actually false. The power of a test is calculated as 1 - \(\beta\). A commonly used power level is 0.8 (or 80%)

Add code to *Report > Rmd* to (re)create the sample size calculations by clicking the icon on the bottom left of your screen or by pressing `ALT-enter`

on your keyboard.

For an overview of related R-functions used by Radiant for sampling and sample size calculations see *Design > Sample*

The key functions from the `pwr`

package used in the `sample_size_comp`

tool are `pwr.t2n.test`

, `pwr.t.test`

, `pwr.2p.test`

, `pwr.2p2n.test`

, and `pwr.2p2n.test`

.