# fix_sample_pow: Simulation of the sample size , the type I error rate and the... In vanLunteren/plan_norm: R-tool for planning clinical studies on normally distributed data

## Description

This is an auxiliary function. It calculates the sample size , simulated type I error rate and the simulated power of a fixed-sample design. The originally planned sample size is calculated on the basis of an assumed standard deviation. A distinction is made between one-sided and two-sided tests. The test statistic is compared to the quantiles of the t-distribution.

## Usage

 ```1 2``` ```fix_sample_pow(sd_ber, delta = 0, Delta, sd, test = 1, alpha = 0.05, beta = 0.2, simu = 10000) ```

## Arguments

 `sd_ber` Vector of numbers. Interval of an area for the actual standard deviation in the data. `delta` Number. Expectation difference of two samples. If you select a Test for superiority/ difference then select 'delta = 0'. Only if you select a Test for non-inferiority you can select 'delta != 0'. Attention: If you chose 'test = 1' and 'delta != 0', the test for non-inferiority will automatically be applied. If not specified, delta is set to 0. `Delta` Number. Relevant difference of expected values in the alternative hypothesis. `sd` Number. Assumed standard deviation of the data. Used to calculate the originally planned sample size. `test` Number. What type of hypothesis test should be performed, one-sided (Superiority/ Non-Inferiority test) or two-sided (Test for difference). One-sided (test = 1): Superiortity H0: mu_x - mu_y <= 0 vs. H1: mu_x - mu_y >0 Non-Inferiority H0: mu_x - mu_y >= delta vs. H1: mu_x - mu_y < delta Two-sided (test = 2): Difference H0: |mu_x - mu_y| = 0 vs. H1: |mu_x - mu_y| != 0 Attention: Choice of delta. (see `delta`) If not specified, the one-Sided Test (Superiority/ Non-Inferiority Test) is used. `alpha` Number. Desired alpha-level of the test. If not specified, alpha is set to 0.05. `beta` Number. Acceptable beta error of the test. If not specified, beta is set to 0.2. `simu` Number. How many simulations should be performed? If not specified, simu is set to 10000.

## Value

This function only creates the sample size, type I error rate and Power values for multiple actual standard deviation values.
The output is used in the function sample_pow to visualize the sample size, the type I error rate and the power.

## Author(s)

Csilla van Lunteren

@seealso `fix_calc`

vanLunteren/plan_norm documentation built on May 20, 2019, 12:32 p.m.