perm.ind.test: Permutation Independence Test
In wPerm: Permutation Tests

Description Usage Arguments Details Value Author(s) Examples

Performs a permutation (randomization) test for independence of two variables, using chi-square as the test statistic.

1 2	perm.ind.test(x, type = c("cont", "flat", "raw"), var.names = NULL, R = 9999)

`x`	a data frame (see details below).
`type`	a character string indicating the type of data frame; must be one of "cont" (default), "flat", or "raw".
`var.names`	an optional character string of length two that gives the names of the variables under consideration; if omitted Var.1 and Var.2 are used.
`R`	number of replications (default = 9999).

The null hypothesis is that the two variables are not associated (i.e., are independent). The alternative hypothesis is that the two variables are associated (i.e., are dependent).

Types of data frames permitted:

cont: In this type of data frame, the first variable gives the possible values of one of the two variables under consideration. The remaining variables of the data frame give the observed frequencies.

flat: This type of data frame consists of three variables. The first two variables give the pairs of possible values of the two variables under consideration; the third variable of the data frame gives the frequencies of the pairs.

raw: This type of data frame consists of two variables, which give the raw data of the two variables under consideration.

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

`Perm.values`	the values of chi-square obtained from the permutations.
`Header`	the main title for the output.
`Variable.1`	the name of the first variable or Var.1
`Variable.2`	the name of the second variable or Var.2
`Statistic`	the statistic used for the permutation test; here, always chi.square.
`Observed`	the value of the chi-square statistic for the observed data.
`n`	the sample size.
`Null`	the null hypothesis; here, always nonassociated.
`Alternative`	the alternative hypothesis; here, always associated.
`P.value`	the P-value or a statement like P < 0.001.
`p.value`	the P-value.

Neil A. Weiss

# Religious belief vs education for a sample of 509 people.
data("relig.and.ed")
str(relig.and.ed)
relig.and.ed
# Note that relig.and.ed is in the form of a flat contingency table ("flat").

# Permutation independence test to decide whether an association exists
# between religiosity and education, using 999 replications.
perm.ind.test(relig.and.ed, "flat", c("Religiosity", "Education"), 999)

# Social class vs nursery-rhyme knowledge for a sample of 66 grade-school
# children.
data("learning")
str(learning)
learning
# Note that the learning data is in the form of a contingency table ("cont").

# Permutation independence test to decide whether an association exists
# between social class and nursery-rhyme knowledge, using 999 replications.
perm.ind.test(learning, "cont", c("Social class", "Nursery-rhyme knowledge"), 999)
# Or, equivalently, since "cont" is the default "type":
perm.ind.test(learning, var.names = c("Social class", "Nursery-rhyme knowledge"), R = 999)

'data.frame':	12 obs. of  3 variables:
 $ RELIGIOUSITY: Factor w/ 4 levels "Religious","Not religious",..: 1 2 3 4 1 2 3 4 1 2 ...
 $ EDUCATION   : Factor w/ 3 levels "Basic","Secondary",..: 1 1 1 1 2 2 2 2 3 3 ...
 $ COUNT       : int  77 23 8 6 149 56 24 15 78 36 ...
    RELIGIOUSITY EDUCATION COUNT
1      Religious     Basic    77
2  Not religious     Basic    23
3        Atheist     Basic     8
4     Don't know     Basic     6
5      Religious Secondary   149
6  Not religious Secondary    56
7        Atheist Secondary    24
8     Don't know Secondary    15
9      Religious  Advanced    78
10 Not religious  Advanced    36
11       Atheist  Advanced    29
12    Don't know  Advanced     8


 RESULTS OF PERMUTATION INDEPENDENCE TEST
 BASED ON 999 REPLICATIONS 

    SUMMARY  Variable.1 Variable.2   n  Statistic Observed
 STATISTICS Religiosity  Education 509 chi.square 13.32231

 HYPOTHESIS          Null Alternative P.value
       TEST nonassociated  associated    0.04


'data.frame':	2 obs. of  4 variables:
 $ SOCIAL_CLASS: Factor w/ 2 levels "Middle","Working": 1 2
 $ A_few       : int  4 5
 $ Some        : int  13 11
 $ Lots        : int  15 18
  SOCIAL_CLASS A_few Some Lots
1       Middle     4   13   15
2      Working     5   11   18


 RESULTS OF PERMUTATION INDEPENDENCE TEST
 BASED ON 999 REPLICATIONS 

    SUMMARY   Variable.1              Variable.2  n  Statistic  Observed
 STATISTICS Social class Nursery-rhyme knowledge 66 chi.square 0.4903493

 HYPOTHESIS          Null Alternative P.value
       TEST nonassociated  associated   0.802




 RESULTS OF PERMUTATION INDEPENDENCE TEST
 BASED ON 999 REPLICATIONS 

    SUMMARY   Variable.1              Variable.2  n  Statistic  Observed
 STATISTICS Social class Nursery-rhyme knowledge 66 chi.square 0.4903493

 HYPOTHESIS          Null Alternative P.value
       TEST nonassociated  associated   0.779