# R/ss.aipe.smd.upper.R In MBESS: The MBESS R Package

#### Documented in ss.aipe.smd.upper

```ss.aipe.smd.upper <- function(delta, conf.level, width, ...)
{
alpha <- 1-conf.level

# Initial starting value for n using the z distribution.
n.0 <- 2*(qnorm(1-alpha/2)/width)^2

# Second starting value for n using the central t distribiton.
n <- 2*((qt(1-alpha/2, 2*n.0-2))/width)^2

# Measures the discrepency between the inital and second starting values.
Difference <- abs(n-n.0)

while(Difference > 0)
{
n.p <- n
n <- 2*((qt(1-alpha/2, 2*n-2))/width)^2
Difference <- abs(n - n.p)
}
n <- ceiling(n)

# To ensure that the initial n is not too big (may happen with small noncentral values).
n <- n-5

# Initial estimate of noncentral value.
# This is literally the theoretical t-value given delta and the initial estimate of sample size.
lambda.0 <- delta*sqrt(n/2)

# Initial confidence limits.
Limits.0 <- ci.smd(ncp=lambda.0, n.1=n, n.2=n, conf.level=1-alpha)

# Initial half-width for upper limit.
Diff.width.Upper.Bound <- abs(Limits.0\$Upper - delta) - width

while(Diff.width.Upper.Bound > 0)
{
n <- n + 1
lambda <- delta*sqrt(n/2)
Limits <- ci.smd(ncp=lambda, n.1=n, n.2=n, conf.level=1-alpha)
Current.Upper.width <- abs(Limits\$Upper-delta)
Diff.width.Upper.Bound <- Current.Upper.width - width
}
return(n)
}
```

## Try the MBESS package in your browser

Any scripts or data that you put into this service are public.

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.