# CramerV: Cramer's V, Pearson's Contingency Coefficient and Phi... In DescTools: Tools for Descriptive Statistics

## Description

Calculate Cramer's V, Pearson's contingency coefficient and phi, Yule's Q and Y and Tschuprow's T of x, if x is a table. If both, x and y are given, then the according table will be built first.

## Usage

 1 2 3 4 5 6 7 8 Phi(x, y = NULL, ...) ContCoef(x, y = NULL, correct = FALSE, ...) CramerV(x, y = NULL, conf.level = NA, method = c("ncchisq", "ncchisqadj", "fisher", "fisheradj"), ...) YuleQ(x, y = NULL, ...) YuleY(x, y = NULL, ...) TschuprowT(x, y = NULL, ...) 

## Arguments

 x can be a numeric vector, a matrix or a table. y NULL (default) or a vector with compatible dimensions to x. If y is provided, table(x, y, ...) is calculated. conf.level confidence level of the interval. This is only implemented for Cramer's V. If set to NA (which is the default) no confidence interval will be calculated. See examples for calculating bootstrap intervals. method string defining the method to calculate confidence intervals for Cramer's V. One out of "ncchisq" (using noncentral chisquare), "ncchisqadj", "fisher" (using fisher z transformation), "fisheradj" (using fisher z transformation and bias correction). Default is "ncchisq". correct logical. This argument only applies to ContCoef and indicates, whether the Sakoda's adjusted Pearson's C should be returned. Default is FALSE. ... further arguments are passed to the function table, allowing i.e. to set useNA.

## Details

For x either a matrix or two vectors x and y are expected. In latter case table(x, y, ...) is calculated. The function handles NAs the same way the table function does, so tables are by default calculated with NAs omitted.

A provided matrix is interpreted as a contingency table, which seems in the case of frequency data the natural interpretation (this is e.g. also what chisq.test expects).

Use the function PairApply (pairwise apply) if the measure should be calculated pairwise for all columns. This allows matrices of association measures to be calculated the same way cor does. NAs are by default omitted pairwise, which corresponds to the pairwise.complete option of cor. Use complete.cases, if only the complete cases of a data.frame are to be used. (see examples)

The maximum value for Phi is √(min(r, c) - 1). The contingency coefficient goes from 0 to √(\frac{min(r, c) - 1}{min(r, c)}). For the corrected contingency coefficient and for Cramer's V the range is 0 to 1.
A Cramer's V in the range of [0, 0.3] is considered as weak, [0.3,0.7] as medium and > 0.7 as strong. The minimum value for all is 0 under statistical independence.

## Value

a single numeric value if no confidence intervals are requested,
and otherwise a numeric vector with 3 elements for the estimate, the lower and the upper confidence interval

## Author(s)

Andri Signorell <[email protected]>,
Michael Smithson <[email protected]> (confidence intervals for Cramer V)

## References

Yule, G. Uday (1912) On the methods of measuring association between two attributes. Journal of the Royal Statistical Society, LXXV, 579-652

Tschuprow, A. A. (1939) Principles of the Mathematical Theory of Correlation, translated by M. Kantorowitsch. W. Hodge & Co.

Cramer, H. (1946) Mathematical Methods of Statistics. Princeton University Press

Agresti, Alan (1996) Introduction to categorical data analysis. NY: John Wiley and Sons

Sakoda, J.M. (1977) Measures of Association for Multivariate Contingency Tables, Proceedings of the Social Statistics Section of the American Statistical Association (Part III), 777-780.

Smithson, M.J. (2003) Confidence Intervals, Quantitative Applications in the Social Sciences Series, No. 140. Thousand Oaks, CA: Sage. pp. 39-41

table, PlotCorr, PairApply, Assocs

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 tab <- table(d.pizza$driver, d.pizza$wine_delivered) Phi(tab) ContCoef(tab) CramerV(tab) TschuprowT(tab) # just x and y CramerV(d.pizza$driver, d.pizza$wine_delivered) # data.frame PairApply(d.pizza[,c("driver","operator","area")], CramerV, symmetric = TRUE) # useNA is passed to table PairApply(d.pizza[,c("driver","operator","area")], CramerV, useNA="ifany", symmetric = TRUE) d.frm <- d.pizza[,c("driver","operator","area")] PairApply(d.frm[complete.cases(d.frm),], CramerV, symmetric = TRUE) m <- as.table(matrix(c(2,4,1,7), nrow=2)) YuleQ(m) YuleY(m) # Bootstrap confidence intervals for Cramer's V # http://support.sas.com/documentation/cdl/en/statugfreq/63124/PDF/default/statugfreq.pdf, p. 1821 tab <- as.table(rbind( c(26,26,23,18, 9), c( 6, 7, 9,14,23))) d.frm <- Untable(tab) n <- 1000 idx <- matrix(sample(nrow(d.frm), size=nrow(d.frm) * n, replace=TRUE), ncol=n, byrow=FALSE) v <- apply(idx, 2, function(x) CramerV(d.frm[x,1], d.frm[x,2])) quantile(v, probs=c(0.025,0.975)) # compare this to the analytical ones CramerV(tab, conf.level=0.95) 

### Example output

[1] 0.1328222
[1] 0.1316659
[1] 0.1328222
[1] 0.08486583
[1] 0.1328222
driver   operator       area
driver   1.0000000 0.23585686 0.65018461
operator 0.2358569 1.00000000 0.08670047
area     0.6501846 0.08670047 1.00000000
driver   operator       area
driver   1.0000000 0.20253639 0.53066544
operator 0.2025364 1.00000000 0.07847762
area     0.5306654 0.07847762 1.00000000
driver  operator      area
driver   1.0000000 0.2345141 0.6504665
operator 0.2345141 1.0000000 0.0869935
area     0.6504665 0.0869935 1.0000000
[1] 0.5555556
[1] 0.303337
2.5%     97.5%
0.2928624 0.5585503
Cramer V    lwr.ci    upr.ci
0.4064888 0.2211672 0.5410622


DescTools documentation built on Aug. 14, 2018, 5:05 p.m.