# asymp.test: Asymptotic tests In asympTest: A Simple R Package for Classical Parametric Statistical Tests and Confidence Intervals in Large Samples

## Description

Performs one and two sample asymptotic (no gaussian assumption on distribution) parametric tests on vectors of data.

## Usage

 ```1 2 3 4 5 6 7 8``` ```asymp.test(x,...) ## Default S3 method: asymp.test(x, y = NULL, parameter = c("mean", "var", "dMean", "dVar", "rMean", "rVar"), alternative = c("two.sided", "less", "greater"), reference = 0, conf.level = 0.95, rho = 1, ...) ## S3 method for class 'formula' asymp.test(formula, data, subset, na.action, ...) ```

## Arguments

 `x` a (non-empty) numeric vector of data values. `y` an optional (non-empty) numeric vector of data values. `parameter` a character string specifying the parameter under testing, must be one of "mean", "var", "dMean" (default), "dVar", "rMean", "rVar" `alternative` a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. `reference` a number indicating the reference value of the parameter (difference or ratio true value for two sample test) `conf.level` confidence level of the interval. `rho` optional parameter (only used for parameters "dMean" and "dVar") for penalization (or enhancement) of the contribution of the second parameter. `formula` a formula of the form `lhs ~ rhs` where `lhs` is a numeric variable giving the data values and `rhs` a factor with two levels giving the corresponding groups. `data` an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`. `subset` an optional vector specifying a subset of observations to be used. `na.action` a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`. `...` further arguments to be passed to or from methods.

## Details

Asymptotic parametric test and confidence intervals are based on the following unified statistic :

est(theta)(Y)-theta / est(var(est(theta)))(Y)

which asymptotically follows a N(0,1).

theta stands for the parameter under testing (mean/variance, difference/ratio of means or variances).

The term est(var(est(theta))) is calculated by the ad-hoc seTheta function (see `seMean`).

## Value

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

 ` statistic ` the value of the unified θ statistic. ` p.value ` the p-value for the test. ` conf.int ` a confidence interval for the parameter appropriate to the specified alternative hypothesis. ` estimate ` the estimated parameter depending on whether it wasa one-sample test or a two-sample test (in which case the estimated parameter can be a difference/ratio in means/variances). ` null.value ` the specified hypothesized value of parameter depending on whether it was a one-sample test or a two-sample test. ` alternative ` a character string describing the alternative hypothesis. ` method ` a character string indicating what type of asymptotictest was performed. ` data.name ` a character string giving the name(s) of the data.

## Author(s)

J.-F. Coeurjolly, R. Drouilhet, P. Lafaye de Micheaux, J.-F. Robineau

## References

C oeurjolly, J.F. Drouilhet, R. Lafaye de Micheaux, P. Robineau, J.F. (2009) asympTest: a simple R package for performing classical parametric statistical tests and confidence intervals in large samples, The R Journal

## See Also

`t.test`, `var.test` for normal distributed data.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## one sample x <- rnorm(70, mean = 1, sd = 2) asymp.test(x) asymp.test(x,par="mean",alt="g") asymp.test(x,par="mean",alt="l",ref=2) asymp.test(x,par="var",alt="g") asymp.test(x,par="var",alt="l",ref=2) ## two samples y <- rnorm(50, mean = 2, sd = 1) asymp.test(x,y) asymp.test(x,y,"rMean","l",.75) asymp.test(x,y,"dMean","l",0,rho=.75) asymp.test(x,y,"dVar") ## Formula interface asymp.test(uptake~Type,data=CO2) ```

### Example output

```	One-sample asymptotic mean test

data:  x
statistic = 3.1968, p-value = 0.00139
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
0.3210356 1.3385236
sample estimates:
mean
0.8297796

One-sample asymptotic mean test

data:  x
statistic = 3.1968, p-value = 0.0006949
alternative hypothesis: true mean is greater than 0
95 percent confidence interval:
0.4028282       Inf
sample estimates:
mean
0.8297796

One-sample asymptotic mean test

data:  x
statistic = -4.5083, p-value = 3.267e-06
alternative hypothesis: true mean is less than 2
95 percent confidence interval:
-Inf 1.256731
sample estimates:
mean
0.8297796

One-sample asymptotic variance test

data:  x
statistic = 5.8971, p-value = 1.85e-09
alternative hypothesis: true variance is greater than 0
95 percent confidence interval:
3.400785      Inf
sample estimates:
variance
4.71629

One-sample asymptotic variance test

data:  x
statistic = 3.3963, p-value = 0.9997
alternative hypothesis: true variance is less than 2
95 percent confidence interval:
-Inf 6.031794
sample estimates:
variance
4.71629

Two-sample asymptotic difference of means test

data:  x and y
statistic = -4.1333, p-value = 3.576e-05
alternative hypothesis: true difference of means is not equal to 0
95 percent confidence interval:
-1.7608216 -0.6280426
sample estimates:
difference of means
-1.194432

Two-sample asymptotic ratio of means test

data:  x and y
statistic = -2.6002, p-value = 0.004658
alternative hypothesis: true ratio of means is less than 0.75
95 percent confidence interval:
-Inf 0.6250514
sample estimates:
ratio of means
0.4099273

Two-sample asymptotic difference of (weighted) means test

data:  x and y
statistic = -2.4896, p-value = 0.006394
alternative hypothesis: true difference of (weighted) means is less than 0
95 percent confidence interval:
-Inf -0.2335817
sample estimates:
difference of (weighted) means
-0.6883792

Two-sample asymptotic difference of variances test

data:  x and y
statistic = 4.771, p-value = 1.833e-06
alternative hypothesis: true difference of variances is not equal to 0
95 percent confidence interval:
2.303520 5.515698
sample estimates:
difference of variances
3.909609

Two-sample asymptotic difference of means test

data:  uptake by Type
statistic = 6.5969, p-value = 4.198e-11
alternative hypothesis: true difference of means is not equal to 0
95 percent confidence interval:
8.898332 16.420716
sample estimates:
difference of means
12.65952
```

asympTest documentation built on May 2, 2019, 11:16 a.m.