Description Usage Arguments Details Value Author(s) Examples

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.

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

`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). |

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".

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

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.
``` |

```
'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
```

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