nNormal: Normal distribution sample size (2-sample)
In gsDesign: Group Sequential Design

Description Usage Arguments Details Value Author(s) References See Also Examples

nNormal() computes a fixed design sample size for comparing 2 means where variance is known. T The function allows computation of sample size for a non-inferiority hypothesis. Note that you may wish to investigate other R packages such as the pwr package which uses the t-distr

1 2	nNormal(delta1=1,sd=1.7,sd2=NULL,alpha=.025,beta=.1,ratio=1, sided=1, n=NULL,delta0=0,outtype=1)

`delta1`	difference between sample means under the alternate hypothesis.
`delta0`	difference between sample means under the null hypothesis; normally this will be left as the default of 0.
`ratio`	randomization ratio of experimental group compared to control.
`sided`	1 for 1-sided test (default), 2 for 2-sided test.
`sd`	Standard deviation for the control arm.
`sd2`	Standard deviation of experimental arm; this will be set to be the same as the control arm with the default of `NULL`.
`alpha`	type I error rate. Default is 0.025 since 1-sided testing is default.
`beta`	type II error rate. Default is 0.10 (90% power). Not needed if `n` is provided.
`n`	Sample size; may be input to compute power rather than sample size. If `NULL` (default) then sample size is computed.

delta0default value of 0 is set to test for superiority; negative values used for non-inferiority (assuming delta1>0).

outtype

controls output; see value section below.

nNormal() computes sample size for comparing two normal means when the variance for observations in

If n is NULL (default), total sample size (2 arms combined) is computed. Otherwise, power is computed. If outtype=1 (default), the computed value (sample size or power) is returned in a scalar or vector. If outtype=2, a data frame with sample sizes for each arm (n1, n2)is returned; if n is not input as NULL, a third variable, Power, is added to the output data frame. If outtype=3, a data frame with is returned with the following columns:

`n`	A vector with total samples size required for each event rate comparison specified
`n1`	A vector of sample sizes for group 1 for each event rate comparison specified
`n2`	A vector of sample sizes for group 2 for each event rate comparison specified
`alpha`	As input
`sided`	As input
`beta`	As input; if `n` is input, this is computed
`Power`	If `n=NULL` on input, this is `1-beta`; otherwise, the power is computed for each sample size input
`sd`	As input
`sd2`	As input
`delta1`	As input
`delta0`	As input
`se`	standard error for estimate of difference in treatment group means

Keaven Anderson keaven_anderson@merck.com

Lachin JM (1981), Introduction to sample size determination and power analysis for clinical trials. Controlled Clinical Trials 2:93-113.

Snedecor GW and Cochran WG (1989), Statistical Methods. 8th ed. Ames, IA: Iowa State University Press.

gsDesign package overview

# EXAMPLES
# equal variances
nNormal(delta1=.5,sd=1.1,alpha=.025,beta=.2)
# unequal variances
nNormal(delta1=.5,sd=1.1,sd2=2,alpha=.025,beta=.2)
# unequal sample sizes
nNormal(delta1=.5,sd=1.1,alpha=.025,beta=.2, ratio=2)
# non-inferiority assuming a better effect than null
nNormal(delta1=.5,delta0=-.1,sd=1.2)