effectsize (version 0.4.1)

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

Description

Convert between Chi square, (\(\chi^2\)), Cramer's V, phi (\(\phi\)) 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).

CI Contains Zero

Special care should be taken when interpreting CIs with a lower bound equal to (or small then) 0, and even more care should be taken when the upper bound is equal to (or small then) 0 (Steiger, 2004; Morey et al., 2016).

Confidence Intervals

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

Details

These functions use the following formulae:

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

$$Cramer's V = \phi / \sqrt{min(nrow,ncol)-1}$$

For adjusted versions, see Bergsma, 2013.

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.

See Also

Other effect size from test statistic: F_to_eta2(), t_to_d()

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)
)
# }