# triangular.test.norm: Triangular Test for Normal Data In OPDOE: Optimal Design of Experiments

## Description

Performs a sequential test, compares means of two normally distributed groups.

## Usage

 ```1 2 3``` ```triangular.test.norm(x, y = NULL, mu0 = NULL, mu1, mu2 = NULL, delta = NULL, sigma = NULL, sigma2 = NULL, alpha = 0.05, beta = 0.1, plot = TRUE) ```

## Arguments

 `x` initial data for group `x`, at least 1 entry. `y` initial data for group `y`, at least 1 entry for a two sample test, otherwise omitted. `mu0` specifies Null and alternative hypothesis, see Details below. `mu1` specifies Null and alternative hypothesis, see Details below. `mu2` specifies Null and alternative hypothesis, see Details below. `delta` The minimum difference to be detected, alternative way to specify `mu2=m1+delta`, see above, use either this or `mu2`. `sigma` prior sigma. `sigma2` prior sigma for group 2 if different than for grouop 1. `alpha` Risk of 1st kind `beta` Risk of 2nd kind `plot` logical, indicates whether a initial plot should be generated.

## Details

One-sample:

This function performs a one- or two-sided sequential Test for μ=\code{mu1} versus

μ>\code{mu2}, if `mu2` > `mu1` (one-sided)

μ<\code{mu2}, if `mu2` < `mu1` (one-sided)

μ<\code{mu0} or μ>\code{mu2}, if `mu2` > `mu1` and `mu0` < `mu1` (two-sided, possibly unsymmetric)

Two-sample:

This function performs a one- or two-sided sequential Test for equal means μ_1=\code{mu1} μ_2=\code{mu1} in both groups versus

μ_2>\code{mu2}, if `mu2` > `mu1` (one-sided)

μ_2<\code{mu2}, if `mu2` < `mu1` (one-sided)

μ_2<\code{mu0} or μ_2>\code{mu2}, if `mu2` > `mu1` and `mu0` < `mu1` (two-sided, possibly unsymmetric)

## Value

An object of class `triangular.test`, to be used for later update steps.

## Note

A two-sided test may be specified by supplying both `mu1` and `mu2`, even unsymmetric if needed.

## Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

## References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

`triangular.test`, `triangular.test.prop`, `update.triangular.test`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```data(heights) attach(heights) # a symmetric two sided alternative: tt <- triangular.test.norm(x=female[1:3], y=male[1:3], mu1=170,mu2=176,mu0=164, alpha=0.05, beta=0.2,sigma=7) # Test is yet unfinished, add the remaining values step by step: tt <- update(tt,x=female[4]) tt <- update(tt,y=male[4]) tt <- update(tt,x=female[5]) tt <- update(tt,y=male[5]) tt <- update(tt,x=female[6]) tt <- update(tt,y=male[6]) tt <- update(tt,x=female[7]) tt <- update(tt,y=male[7]) # Test is finished now # an unsymmetric two sided alternative: tt2 <- triangular.test.norm(x=female[1:3], y=male[1:3], mu1=170,mu2=180,mu0=162, alpha=0.05, beta=0.2,sigma=7) tt2 <- update(tt2,x=female[4]) ```