rss.z.test {generalRSS}R Documentation

RSS z-test for one-sample and two-sample problems

Description

The rss.z.test function performs one- and two-sample z-tests on ranked set sample data using normal approximation, with options for specifying the confidence level, alternative hypothesis, and hypothesized mean or mean difference.

Usage

rss.z.test(
  data1,
  data2 = NULL,
  alpha = 0.05,
  alternative = "two.sided",
  mu0 = 0
)

Arguments

data1

A numeric data frame of ranked set samples with columns rank for ranks and y for data values.

data2

An optional numeric data frame of ranked set samples with columns rank for ranks and y for data values (for two-sample problem).

alpha

A numeric value specifying the confidence level for the interval.

alternative

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

mu0

A numeric value indicating the hypothesized value of the mean (for a one-sample problem) or the difference in means (for a two-sample problem).

Details

This function performs a z-test on ranked set sample data for both one-sample and two-sample mean comparison problems, using normal approximation. For a one-sample test, only data1 is needed, provided as a data frame with columns rank and y. For a two-sample test, both data1 and data2 must be supplied, each as data frames with rank and y columns. The function computes the test statistic, confidence interval, and p-value based on the provided RSS data and specified parameters.

Value

RSS_mean

The RSS mean estimate for a one-sample problem or a vector of RSS mean estimates for each group in a two-sample problem.

CI

The confidence interval for the population mean for a one-sample problem or for the mean difference in a two-sample problem.

z

The z-statistic for the test.

p.value

The p-value for the test.

References

Chen, Z., Bai Z., Sinha B. K. (2003). Ranked Set Sampling: Theory and Application. New York: Springer.

S. Ahn, J. Lim, and X. Wang. (2014) The student’s t approximation to distributions of pivotal statistics from ranked set samples. Journal of the Korean Statistical Society, 43, 643–652.

S. Ahn, X. Wang, C. Moon, and J. Lim. (2024) New scheme of empirical likelihood method for ranked set sampling: Applications to two one sample problems. International Statistical Review.

See Also

rss.simulation: used for simulating Ranked Set Samples (RSS), which can serve as input.

rss.sampling: used for sampling Ranked Set Samples (RSS) from a population data set, providing input data.

Examples

## Balanced RSS with a set size 3 and equal sample sizes of 6 for each stratum,
## using imperfect ranking from a normal distribution with a mean of 0.
rss.data1=rss.simulation(H=3,nsamp=c(6,6,6),dist="normal", rho=0.8,delta=0)

## one-sample z-test
rss.z.test(data1=rss.data1, data2=NULL, alpha=0.05,
alternative="two.sided", mu0=0)

## Unbalanced RSS with a set size 3 and different sample sizes of 6, 10, and 8 for each stratum,
## using imperfect ranking from a normal distribution with a mean of 0.
rss.data2<-rss.simulation(H=3,nsamp=c(6,8,10),dist="normal", rho=0.8,delta=0)

## two-sample z-test
rss.z.test(data1=rss.data1, data2=rss.data2, alpha=0.05,
alternative="two.sided", mu0=0)


[Package generalRSS version 0.1.3 Index]