diffmean.test {LearningStats}

Two Sample Mean Test of Normal Populations

Description

diffmean.test allows to compute hypothesis tests about two population means. The difference between the means of two Normal populations is tested in different scenarios: known or unknown variance, variances assumed equal or different and paired or independent populations.

Usage

diffmean.test(x1, x2, sigma1 = NULL, sigma2 = NULL, sc1 = NULL,
  sc2 = NULL, s1 = NULL, s2 = NULL, n1 = NULL, n2 = NULL,
  var.equal = FALSE, paired = FALSE, alternative = "two.sided",
  alpha = 0.05, plot = TRUE, lwd = 1)

Arguments

x1

a numeric vector of data values or, if single number, estimated mean.

x2

a numeric vector of data values or, if single number, estimated mean.

sigma1

if known, a single numeric value corresponding with one of the population standard deviation.

sigma2

if known, a single numeric value corresponding with the other population standard deviation.

sc1

cuasi-standard deviation of sample x1. By default computes the cuasi-standard deviation of argument x1.

sc2

cuasi-standard deviation of sample x2. By default computes the cuasi-standard deviation of argument x2.

s1

sample standard deviation of sample x1. Defaults to NULL, if provided, it computes the cuasi-standard deviation.

s2

sample standard deviation of sample x2. Defaults to NULL, if provided, it computes the cuasi-standard deviation.

n1

sample size of x1. By default length of argument x1.

n2

sample size of x2. By default length of argument x2.

var.equal

a logical indicating whether to treat the two variances as being equal. Defaults to FALSE.

paired

a logical indicating whether the samples are paired. Defaults to FALSE, if TRUE, then both x1 and x2 must be the same length.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".

alpha

single number in (0,1), corresponding with the significance level.

plot

a logical value indicating whether to display a graph including the test statistic value for the sample, its distribution, the rejection region and p-value.

lwd

single number indicating the line width of the plot.

Details

If sigma1 and sigma2 are given, known population variances formula is applied; the unknown one is used in other case.

If paired is TRUE then both x1 and x2 must be specified and their sample sizes must be the same. If paired is null, then it is assumed to be FALSE.

For var.equal=TRUE, the formula of the pooled variance is \frac{(n1-1)sc1^2+(n2-1)sc2^2}{n1+n2-2}.

Value

A list with class "lstest" and "htest" containing the following components:

statistic

the value of the test statistic.

parameter

the degrees of freedom of the statistic's distribution. NULL for the Normal distribution.

p.value

the p-value of the test.

estimate

the estimated difference in means.

null.value

the value specified by the null.

alternative

a character string describing the alternative.

method

a character string indicating the method used.

data.name

a character string giving the names of the data.

alpha

the significance level.

dist.name

a character string indicating the distribution of the test statistic.

statformula

a character string with the statistic's formula.

reject.region

a character string with the reject region.

Examples

x1 <- rnorm(40, mean = 1.5, sd = 2)
x2 <- rnorm(60, mean = 2, sd = 2)
#equal variances
diffmean.test(x1, x2, var.equal = TRUE)
diffmean.test(mean(x1), mean(x2),
              sc1 = sd(x1), sc2 = sd(x2),
              n1 = 40, n2 = 60, var.equal = TRUE)
x3 <- rnorm(60, mean = 2, sd = 1.5)
#different variances
diffmean.test(x1, x3)
#known standard deviation
diffmean.test(x1, x3, sigma1 = 2, sigma2 = 1.5)
x4 <- x1 + rnorm(40, mean = 0, sd = 0.1)
#paired samples
diffmean.test(x1, x4, paired = TRUE)