# perm.relation: Permutation Test for a Relationship In wPerm: Permutation Tests

## Description

Performs a permutation (randomization) test for a relationship (correlation, association) for two quantitative variables, using Pearson's r (product moment correlation coefficient), Spearman's rho (rank correlation coefficient), or Kendall's tau as the test statistic.

## Usage

 ```1 2 3``` ```perm.relation(x, y, method = c("pearson", "kendall", "spearman"), alternative = c("two.sided", "less", "greater"), R = 9999) ```

## Arguments

 `x` a numeric vector of data values representing the first variable. `y` a numeric vector of data values representing the second variable. `method` a character string indicating which method is to be used for the test; one of "pearson" (default), "kendall", or "spearman". `alternative` a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "less", or "greater". `R` number of replications (default = 9999).

## Details

The null hypothesis is that there is no relationship between the variables.

The possible alternative hypotheses are:

Two tailed ("two.sided"): There is a relationship between the variablesâ€”"relation".

Left tailed ("less"): There is a negative relationship between the variablesâ€”"neg.relation".

Right tailed ("greater"): There is a positive relationship between the variablesâ€”"pos.relation".

## Value

A list with class "perm.two.var" containing the following components:

 `Perm.values ` the values of the test statistic obtained from the permutations. `Header ` the main title for the output. `Variable.1 ` the name of the first variable. `Variable.2 ` the name of the second variable. `n ` the sample size. `Statistic ` the test statistic. `Observed ` the observed value of the test statistic. `Null ` the null hypothesis; here, always no relation. `Alternative ` the alternative hypothesis. `P.value ` the P-value or a statement like P < 0.001. `p.value ` the P-value.

Neil A. Weiss

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# Prices, in euros, of a 50cl bottle of water and distances, in meters, # of convenience stores from the Contemporary Art Museum in El Raval, # Barcelona. data("water") str(water) attach(water) # Permutation test to decide whether a negative relationship exists # between price and distance, using Pearson's r as the test statistic. perm.relation(PRICE, DISTANCE, alternative = "less") # Permutation test to decide whether a negative relationship exists # between price and distance, using Kendall's tau as the test statistic. perm.relation(PRICE, DISTANCE, "kendall", "less") # Permutation test to decide whether a negative relationship exists # between price and distance, using Spearman's rho as the test statistic. perm.relation(PRICE, DISTANCE, "spearman", "less") detach(water) # clean up. ```

### Example output

```'data.frame':	10 obs. of  2 variables:
\$ DISTANCE: num  50 175 270 375 425 580 710 790 890 980
\$ PRICE   : num  1.8 1.2 2 1 1 1.2 0.8 0.6 1 0.85

RESULTS OF PERMUTATION RELATIONSHIP TEST
BASED ON 9999 REPLICATIONS

SUMMARY Variable.1 Variable.2  n   Statistic   Observed
STATISTICS      PRICE   DISTANCE 10 pearson.cor -0.7271081

HYPOTHESIS        Null  Alternative P.value
TEST no.relation neg.relation  0.0069

RESULTS OF PERMUTATION RELATIONSHIP TEST
BASED ON 9999 REPLICATIONS

SUMMARY Variable.1 Variable.2  n   Statistic   Observed
STATISTICS      PRICE   DISTANCE 10 kendall.cor -0.5820252

HYPOTHESIS        Null  Alternative P.value
TEST no.relation neg.relation  0.0118

RESULTS OF PERMUTATION RELATIONSHIP TEST
BASED ON 9999 REPLICATIONS

SUMMARY Variable.1 Variable.2  n    Statistic   Observed
STATISTICS      PRICE   DISTANCE 10 spearman.cor -0.7570127

HYPOTHESIS        Null  Alternative P.value
TEST no.relation neg.relation  0.0075
```

wPerm documentation built on May 2, 2019, 3:02 a.m.