# chisq: Pearson's chi-squared statistic for frequency comparisons... In corpora: Statistics and Data Sets for Corpus Frequency Data

## Description

This function computes Pearson's chi-squared statistic (often written as X^2) for frequency comparison data, with or without Yates' continuity correction. The implementation is based on the formula given by Evert (2004, 82).

## Usage

 `1` ```chisq(k1, n1, k2, n2, correct = TRUE, one.sided=FALSE) ```

## Arguments

 `k1` frequency of a type in the first corpus (or an integer vector of type frequencies) `n1` the sample size of the first corpus (or an integer vector specifying the sizes of different samples) `k2` frequency of the type in the second corpus (or an integer vector of type frequencies, in parallel to `k1`) `n2` the sample size of the second corpus (or an integer vector specifying the sizes of different samples, in parallel to `n1`) `correct` if `TRUE`, apply Yates' continuity correction (default) `one.sided` if `TRUE`, compute the signed square root of X^2 as a statistic for a one-sided test (see details below; the default value is `FALSE`)

## Details

The X^2 values returned by this function are identical to those computed by `chisq.test`. Unlike the latter, `chisq` accepts vector arguments so that a large number of frequency comparisons can be carried out with a single function call.

The one-sided test statistic (for `one.sided=TRUE`) is the signed square root of X^2. It is positive for k_1/n_1 > k_2/n_2 and negative for k_1/n_1 < k_2/n_2. Note that this statistic has a standard normal distribution rather than a chi-squared distribution under the null hypothesis of equal proportions.

## Value

The chi-squared statistic X^2 corresponding to the specified data (or a vector of X^2 values). This statistic has a chi-squared distribution with df=1 under the null hypothesis of equal proportions.

Stefan Evert

## References

Evert, Stefan (2004). The Statistics of Word Cooccurrences: Word Pairs and Collocations. Ph.D. thesis, Institut für maschinelle Sprachverarbeitung, University of Stuttgart. Published in 2005, URN urn:nbn:de:bsz:93-opus-23714. Available from http://www.collocations.de/phd.html.

`chisq.pval`, `chisq.test`, `cont.table`