RT2SAMP: Randomization Test of the Mean Difference between Two Samples

In ganava4/rbmc: Randomization, Bootstrap and Monte Carlo Methods in Biology

Randomization Test of the Mean Difference between Two Samples

Description

RT2SAMP carries out a two sample randomization test on the mean difference between two samples. A randomization confidence interval for the mean difference between two source populations can also be determined.

Usage

RT2SAMP(
  x,
  y,
  NRAND = 4999,
  alt = "two",
  CI = FALSE,
  silent = FALSE,
  seed = NULL
)

Arguments

x	a (non-empty) numeric vector of data values.
y	a (non-empty) numeric vector of data values.
NRAND	numeric; the number of randomizations (permutations).
alt	a character string specifying the alternative hypothesis, must be one of "two" (two-sided, the default), "greater" or "less".
CI	a logical variable indicating whether approximate 95% and 99% randomization confidence intervals will be calculated (TRUE) or not (FALSE).
silent	a logical variable indicating whether calculation results are printed to the R console (silent = FALSE). If TRUE then calculation results are not printed to the R console (useful for simulations)
seed	a single value, interpreted as an integer, or NULL (see "Details").

Details

The procedure (1) calculates the mean scores for vectors x and y, and the difference D[0] between these; then (2) length(x) and length(y) observations are randomly reallocated to the first and second group, respectively, using the sample function. Step (2) is repeated NRAND times to find the randomization distribution of D differences. alt = "greater" is the alternative that x has a larger mean than y.

The randomization test allows confidence intervals to be placed on treatment effects (when CI = TRUE), as described in Manly and Navarro (2021, Section 1.4). If confidence limits are needed, NRAND should be a large enough number (probably 4999 or more). The upper percentage points (percentages of randomization differences greater than or equal to the observed between x and y means) can be determined for a range of trial values for L and U, which, when subtracted from the x, just avoid giving a significant difference between the two sample means. The upper percentage points (percentages of randomization differences greater than or equal to the observed difference between x and y) can be determined for a range of trial values for L, and linear interpolation is used to determine the value of L to be substracted from the x measurements producing a difference between x and y that is on the borderline of being significantly large at about the 2.5% or 0.5%. Analogously, the lower percentage points (the percentages of randomization differences less than or equal to the observed difference between x and y means) can be determined for some trial values of U. Again, linear interpolation is used to determine the value of U to be substracted from the x measurements producing a difference between x and y that is on the borderline of being significantly small at about the 2.5% or 0.5% level.

seed is a way to call the set.seed function, "the recommended way to specify seeds" in random number generation.

The function summary.RT is used to obtain and print a summary of the results, and a plot.RT method is available for displaying the randomization distribution of mean differences.

Value

The function returns a RT result object (list)

Author(s)

Jorge Navarro-Alberto

References

Manly, B.F.J. and Navarro-Alberto, J.A. (2021) Randomization, Bootstrap and Monte Carlo Methods in Biology. 4th Edition. Chapman and Hall/ CRC Press.

See Also

summary.RT and the main plotting function plot.RT

Examples

# Example in Manly and Navarro Alberto (2021), Section 1.1
male <- jackals$Mand.length[jackals$Sex=="M"]
female <- jackals$Mand.length[jackals$Sex=="F"]
jackals.RT2 <- RT2SAMP(male, female, alt="greater")

ganava4/rbmc documentation built on April 24, 2022, 12:14 a.m.