# Triangular Test for Normal Data Performs a sequential test, compares means of two normally distributed groups. ```r 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 $\mu=\code{mu1}$ versus $\mu>\code{mu2}$, if `mu2` > `mu1` (one-sided) $\mu<\code{mu2}$, if `mu2` < `mu1` (one-sided) $\mu<\code{mu0}$ or $\mu>\code{mu2}$, 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 $\mu_1=\code{mu1}$ $\mu_2=\code{mu1}$ in both groups versus $\mu_2>\code{mu2}$, if `mu2` > `mu1` (one-sided) $\mu_2<\code{mu2}$, if `mu2` < `mu1` (one-sided) $\mu_2<\code{mu0}$ or $\mu_2>\code{mu2}$, if `mu2` > `mu1` and `mu0` < `mu1` (two-sided, possibly unsymmetric) ## Returns 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. ## References Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011 ## Author(s) Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt ## See Also `triangular.test`, `triangular.test.prop`, `update.triangular.test` ## Examples ```r 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]) ```

triangular.test.norm function