# power.hsu.t.test: Power calculations for two sample Hsu t test In stamats/MKpower: Power Analysis and Sample Size Calculation

## Description

Compute the power of the two-sample Hsu t test, or determine parameters to obtain a target power; see Section 7.4.4 in Hedderich and Sachs (2016),

## Usage

 ```1 2 3``` ```power.hsu.t.test(n = NULL, delta = NULL, sd1 = 1, sd2 = 1, sig.level = 0.05, power = NULL, alternative = c("two.sided", "one.sided"), strict = FALSE, tol = .Machine\$double.eps^0.25) ```

## Arguments

 `n` number of observations (per group) `delta` (expected) true difference in means `sd1` (expected) standard deviation of group 1 `sd2` (expected) standard deviation of group 2 `sig.level` significance level (Type I error probability) `power` power of test (1 minus Type II error probability) `alternative` one- or two-sided test. Can be abbreviated. `strict` use strict interpretation in two-sided case `tol` numerical tolerance used in root finding, the default providing (at least) four significant digits.

## Details

Exactly one of the parameters `n`, `delta`, `power`, `sd1`, `sd2` and `sig.level` must be passed as `NULL`, and that parameter is determined from the others. Notice that the last three have non-NULL defaults, so NULL must be explicitly passed if you want to compute them.

If `strict = TRUE` is used, the power will include the probability of rejection in the opposite direction of the true effect, in the two-sided case. Without this the power will be half the significance level if the true difference is zero.

## Value

Object of class `"power.htest"`, a list of the arguments (including the computed one) augmented with `method` and `note` elements.

## Note

The function and its documentation was adapted from `power.t.test` implemented by Peter Dalgaard and based on previous work by Claus Ekstroem.

`uniroot` is used to solve the power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.

## Author(s)

Matthias Kohl [email protected]

## References

J. Hedderich, L. Sachs. Angewandte Statistik: Methodensammlung mit R. Springer 2016.

`power.welch.t.test`, `power.t.test`, `t.test`, `uniroot`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ``` ## more conservative than classical or Welch t-test power.hsu.t.test(n = 20, delta = 1) power.hsu.t.test(power = .90, delta = 1) power.hsu.t.test(power = .90, delta = 1, alternative = "one.sided") ## sd1 = 0.5, sd2 = 1 power.welch.t.test(delta = 0.5, sd1 = 0.5, sd2 = 1, power = 0.9) power.hsu.t.test(delta = 0.5, sd1 = 0.5, sd2 = 1, power = 0.9) if(require(MKinfer)){ ## empirical check M <- 10000 ps <- numeric(M) for(i in seq_len(M)){ x <- rnorm(55, mean = 0, sd = 0.5) y <- rnorm(55, mean = 0.5, sd = 1.0) ps[i] <- hsu.t.test(x, y)\$p.value } ## empirical power sum(ps < 0.05)/M } ```