# one_sample: Deal with one (normal) sample In OneTwoSamples: Deal with One and Two (Normal) Samples

 one_sample R Documentation

## Deal with one (normal) sample

### Description

Deal with one sample `x`, especially normal. Report descriptive statistics, plot, interval estimation and test of hypothesis of `x`.

### Usage

``````one_sample(x, mu = Inf, sigma = -1, side = 0, alpha = 0.05)
``````

### Arguments

 `x` A numeric vector. `mu` `mu` plays two roles. In two sided or one sided interval estimation (or test of hypothesis) of `sigma^2` of one normal sample, `mu` is the population mean. When it is known, input it, and the function computes the interval endpoints (or chi-square statistic) using a chi-square distribution with degree of freedom `n`. When it is unknown, ignore it (the default), and the function computes the interval endpoints (or chi-square statistic) using a chi-square distribution with degree of freedom `n-1`. In two sided or one sided test of hypothesis of `mu` of one normal sample, `mu` is `mu0` in the null hypothesis, and `mu0 = if (mu < Inf) mu else 0`. `sigma` `sigma` plays two roles. In two sided or one sided interval estimation (or test of hypothesis) of `mu` of one normal sample, `sigma` is the standard deviation of the population. `sigma>=0` indicates it is known, and the function computes the interval endpoints (or `Z` statistic) using a standard normal distribution. `sigma<0` indicates it is unknown, and the function computes the interval endpoints (or `T` statistic) using a `t` distribution with degree of freedom `n-1`. Default to unknown standard deviation. In two sided or one sided test of hypothesis of `sigma^2` of one normal sample, `sigma` is `sigma0` in the null hypothesis. Default is 1, i.e., `H0: sigma^2 = 1`. `side` `side` plays two roles and is used in four places. In two sided or one sided interval estimation of `mu` of one normal sample, `side` is a parameter used to control whether to compute two sided or one sided interval estimation. When computing the one sided upper limit, input `side = -1`; when computing the one sided lower limit, input `side = 1`; when computing the two sided limits, input `side = 0` (default). In two sided or one sided interval estimation of `sigma^2` of one normal sample, side is a parameter used to control whether to compute two sided or one sided interval estimation. When computing the one sided upper limit, input `side = -1`; when computing the one sided lower limit, input `side = 1`; when computing the two sided limits, input `side = 0` (default). In two sided or one sided test of hypothesis of `mu` of one normal sample, `side` is 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: mu != mu0`; when inputting `side = -1` (or a number < 0), the function computes one sided test of hypothesis, and `H1: mu < mu0`; when inputting `side = 1` (or a number > 0), the function computes one sided test of hypothesis, and `H1: mu > mu0`. In two sided or one sided test of hypothesis of `sigma^2` of one normal sample, `side` is 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: sigma^2 != sigma0^2`; when inputting `side = -1` (or a number < 0), the function computes one sided test of hypothesis, and `H1: sigma^2 < sigma0^2`; when inputting `side = 1` (or a number > 0), the function computes one sided test of hypothesis, and `H1: sigma^2 > sigma0^2`. `alpha` The significance level, a real number in [0, 1]. Default to 0.05. 1-alpha is the degree of confidence.

### Value

A list with the following components:

 `mu_interval ` It contains the results of interval estimation of `mu`. `mu_hypothesis ` It contains the results of test of hypothesis of `mu`. `sigma_interval ` It contains the results of interval estimation of `sigma`. `sigma_hypothesis ` It contains the results of test of hypothesis of `sigma`.

### Author(s)

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

### References

Zhang, Y. Y., Wei, Y. (2013), One and two samples using only an R funtion, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2991/asshm-13.2013.29")}.

### Examples

``````x=rnorm(10, mean = 1, sd = 0.2); x
one_sample(x, mu = 1, sigma = 0.2, side = 1)
one_sample(x, sigma = 0.2, side = 1)
one_sample(x, mu = 1, side = 1)
one_sample(x)
``````

OneTwoSamples documentation built on March 31, 2023, 11:49 p.m.