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Two sided or one sided test of hypothesis of mu1 and mu2 of two normal samples

mean_test2.Rd

Compute the two sided or one sided test of hypothesis of mu1 and mu2 of two normal samples when the population variances are known, unknown equal, or unknown unequal.

Usage

mean_test2(x, y, sigma = c(-1, -1), var.equal = FALSE, side = 0)

Arguments

x

A numeric vector.

y

A numeric vector.

sigma

A numeric vector of length 2, which contains the standard deviations of two populations. When the standard deviations are known, input it, then the function computes the interval endpoints using normal population; when the standard deviations are unknown, ignore it, now we need to consider whether the two populations have equal variances. See var.equal below.

var.equal

A logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

side

A parameter used to control two sided or one sided test of hypothesis. When inputting side = 0 (default), the function computes two sided test of hypothesis, and H1: mu1 != mu2; when inputting side = -1 (or a number < 0), the function computes one sided test of hypothesis, and H1: mu1 < mu2; when inputting side = 1 (or a number > 0), the function computes one sided test of hypothesis, and H1: mu1 > mu2.

Value

A data.frame with variables:

mean

The difference of sample means xb-yb.

df

The degree of freedom.

statistic

The statistic, when all(sigma>=0), statistic = Z; otherwise, statistic = T.

p_value

The P value.

References

Zhang, Y. Y., Wei, Y. (2013), One and two samples using only an R funtion, doi:10.2991/asshm-13.2013.29 .

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
#>  [1] 0.8694650 0.9705661 0.7451797 1.0790655 0.6134213 1.2109006 0.8358040
#>  [8] 0.8724738 0.9693751 0.7167187
y=rnorm(20, mean = 2, sd = 0.3); y
#>  [1] 2.182195 2.026518 1.528918 2.093852 2.195804 1.997613 2.518110 2.625940
#>  [9] 1.892496 1.567363 2.114383 2.027209 2.048629 2.106785 1.892086 1.967412
#> [17] 2.548336 1.411425 2.283795 2.164689
mean_test2(x, y, sigma = c(0.2, 0.3), side = 1)
#>        mean df         Z p_value
#> 1 -1.171381 30 -12.70541       1
mean_test2(x, y, var.equal = TRUE, side = 1)
#>        mean df         T p_value
#> 1 -1.171381 28 -10.86827       1
mean_test2(x, y, side = 1)
#>        mean       df         T p_value
#> 1 -1.171381 27.44942 -13.01289       1