effectsize (version 0.4.0)

chisq_to_phi: Conversion Chi-Squared to Phi or Cramer's V

Description

Convert between Chi square, (${\chi }^2$), Cramer's V, phi ($\varphi$) and Cohen's w for contingency tables or goodness of fit.

Usage

chisq_to_phi(chisq, n, nrow, ncol, ci = 0.95, adjust = FALSE, ...)
chisq_to_cohens_w(chisq, n, nrow, ncol, ci = 0.95, adjust = FALSE, ...)
chisq_to_cramers_v(chisq, n, nrow, ncol, ci = 0.95, adjust = FALSE, ...)
phi_to_chisq(phi, n, ...)

Arguments

chisq

The Chi-squared statistic.

n

Sample size.

nrow, ncol

The number of rows/columns in the contingency table (ignored for Phi when adjust=FALSE and CI=NULL).

ci

Confidence Interval (CI) level

adjust

Should the effect size be bias-corrected? Defaults to FALSE.

...

Arguments passed to or from other methods.

phi

The Phi statistic.

Value

A data frame with the effect size(s) between 0-1, and confidence interval(s).

Details

These functions use the following formulae:

$$\varphi =\sqrt{{\chi }^2/n}$$

$$Crame{r}^{\prime }sV=\varphi /\sqrt{min(nrow,ncol)-1}$$

For adjusted versions, see Bergsma, 2013.

Confidence Intervals

Confidence intervals are estimated using the Noncentrality parameter method; These methods searches for a the best ncp (non-central parameters) for of the noncentral Chi-squared distribution for the desired tail-probabilities, and then convert these ncps to the corresponding effect sizes.

References

• Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61(4), 532-574.

• Bergsma, W. (2013). A bias-correction for Cramer's V and Tschuprow's T. Journal of the Korean Statistical Society, 42(3), 323-328.

Examples

# NOT RUN {
contingency_table <- as.table(rbind(c(762, 327, 468), c(484, 239, 477), c(484, 239, 477)))

chisq.test(contingency_table)
#
#         Pearson's Chi-squared test
#
# data:  ctab
# X-squared = 41.234, df = 4, p-value = 2.405e-08

chisq_to_phi(41.234,
  n = sum(contingency_table),
  nrow = nrow(contingency_table),
  ncol = ncol(contingency_table)
)
chisq_to_cramers_v(41.234,
  n = sum(contingency_table),
  nrow = nrow(contingency_table),
  ncol = ncol(contingency_table)
)

# }