# yuend: Paired samples robust t-tests. In WRS2: A Collection of Robust Statistical Methods

## Description

The function `yuend` performs Yuen's test on trimmed means for dependent samples. `Dqcomhd` compares the quantiles of the marginal distributions associated with two dependent groups via hd estimator. Tied values are allowed. `dep.effect` computes various effect sizes and confidence intervals for two dependent samples (see Details).

## Usage

 ```1 2 3``` ```yuend(x, y, tr = 0.2, ...) Dqcomhd(x, y, q = c(1:9)/10, nboot = 1000, na.rm = TRUE, ...) dep.effect(x, y, tr = 0.2, nboot = 1000, ...) ```

## Arguments

 `x` an numeric vector of data values (e.g. for time 1). `y` an numeric vector of data values (e.g. for time 2). `tr` trim level for the means. `q` quantiles to be compared. `nboot` number of bootstrap samples. `na.rm` whether missing values should be removed. `...` currently ignored.

## Details

The test statistic is a paired samples generalization of Yuen's independent samples t-test on trimmed means.

`dep.effect` computes the following effect sizes:

AKP: robust standardized difference similar to Cohen's d

QS: Quantile shift based on the median of the distribution of difference scores,

QStr: Quantile shift based on the trimmed mean of the distribution of X-Y

SIGN: P(X<Y), probability that for a random pair, the first is less than the second.

## Value

`yuend` returns an object of class `"yuen"` containing:

 `test` value of the test statistic (t-statistic) `p.value` p-value `conf.int` confidence interval `df` degress of freedom `diff` trimmed mean difference `call` function call

`Dqcomhd` returns an object of class `"robtab"` containing:

 `partable` parameter table

`dep.effect` returns a matrix with the null value of the effect size, the estimated effect size, small/medium/large conventions, and lower/upper CI bounds.

## References

Wilcox, R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Elsevier.

`yuen`, `qcomhd`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Cholesterol data from Wilcox (2012, p. 197) before <- c(190, 210, 300,240, 280, 170, 280, 250, 240, 220) after <- c(210, 210, 340, 190, 260, 180, 200, 220, 230, 200) yuend(before, after) set.seed(123) Dqcomhd(before, after, nboot = 200, q = c(0.25, 0.5, 0.75)) set.seed(123) dep.effect(before, after) ```

### Example output

```Call:
yuend(x = before, y = after)

Test statistic: 1.9886 (df = 5), p-value = 0.10343

Trimmed mean difference:  28.33333
95 percent confidence interval:
-8.2918     64.9585

Explanatory measure of effect size: 0.52

Call:
Dqcomhd(x = before, y = after, q = c(0.25, 0.5, 0.75), nboot = 200)

Parameter table:
q n1 n2     est1     est2 est1-est.2   ci.low   ci.up p.crit p.value
1 0.25 10 10 205.9676 196.4354     9.5322  -9.9688 36.4466 0.0500    0.43
2 0.50 10 10 238.8929 211.2158    27.6770   2.4674 47.3345 0.0167    0.03
3 0.75 10 10 271.0781 245.3351    25.7431 -20.9178 52.2341 0.0250    0.27

NULL       Est    S    M    L     ci.low    ci.up
AKP          0.0 0.4331978 0.10 0.30 0.50 -0.2978559 2.071852
QS (median)  0.5 0.8000000 0.54 0.62 0.69  0.3000000 1.000000
QStr         0.5 0.7000000 0.54 0.62 0.69  0.4000000 1.000000
SIGN         0.5 0.3333333 0.46 0.38 0.31  0.0870000 0.619000
```

WRS2 documentation built on July 20, 2021, 9:06 a.m.