| chisq_to_phi {effectsize} | R Documentation |
Convert \chi^2 to \phi and Other Correlation-like Effect Sizes
Description
Convert between \chi^2 (chi-square), \phi (phi), Cramer's
V, Tschuprow's T, Cohen's w,
פ (Fei) and Pearson's C for contingency
tables or goodness of fit.
Usage
chisq_to_phi(
chisq,
n,
nrow = 2,
ncol = 2,
adjust = TRUE,
ci = 0.95,
alternative = "greater",
...
)
chisq_to_cohens_w(
chisq,
n,
nrow,
ncol,
p,
ci = 0.95,
alternative = "greater",
...
)
chisq_to_cramers_v(
chisq,
n,
nrow,
ncol,
adjust = TRUE,
ci = 0.95,
alternative = "greater",
...
)
chisq_to_tschuprows_t(
chisq,
n,
nrow,
ncol,
adjust = TRUE,
ci = 0.95,
alternative = "greater",
...
)
chisq_to_fei(chisq, n, nrow, ncol, p, ci = 0.95, alternative = "greater", ...)
chisq_to_pearsons_c(
chisq,
n,
nrow,
ncol,
ci = 0.95,
alternative = "greater",
...
)
phi_to_chisq(phi, n, ...)
Arguments
chisq |
The |
n |
Total sample size. |
nrow, ncol |
The number of rows/columns in the contingency table. |
adjust |
Should the effect size be corrected for small-sample bias?
Defaults to |
ci |
Confidence Interval (CI) level |
alternative |
a character string specifying the alternative hypothesis;
Controls the type of CI returned: |
... |
Arguments passed to or from other methods. |
p |
Vector of expected values. See |
phi |
The |
Details
These functions use the following formulas:
\phi = w = \sqrt{\chi^2 / n}
\textrm{Cramer's } V = \phi / \sqrt{\min(\textit{nrow}, \textit{ncol}) - 1}
\textrm{Tschuprow's } T = \phi / \sqrt[4]{(\textit{nrow} - 1) \times (\textit{ncol} - 1)}
פ = \phi / \sqrt{[1 / \min(p_E)] - 1}
Where p_E are the expected probabilities.
\textrm{Pearson's } C = \sqrt{\chi^2 / (\chi^2 + n)}
For versions adjusted for small-sample bias of \phi, V, and T,
see Bergsma, 2013.
Value
A data frame with the effect size(s), and confidence interval(s). See
cramers_v().
Confidence (Compatibility) Intervals (CIs)
Unless stated otherwise, confidence (compatibility) intervals (CIs) are
estimated using the noncentrality parameter method (also called the "pivot
method"). This method finds the noncentrality parameter ("ncp") of a
noncentral t, F, or \chi^2 distribution that places the observed
t, F, or \chi^2 test statistic at the desired probability point of
the distribution. For example, if the observed t statistic is 2.0, with 50
degrees of freedom, for which cumulative noncentral t distribution is t =
2.0 the .025 quantile (answer: the noncentral t distribution with ncp =
.04)? After estimating these confidence bounds on the ncp, they are
converted into the effect size metric to obtain a confidence interval for the
effect size (Steiger, 2004).
For additional details on estimation and troubleshooting, see effectsize_CIs.
CIs and Significance Tests
"Confidence intervals on measures of effect size convey all the information
in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility)
intervals and p values are complementary summaries of parameter uncertainty
given the observed data. A dichotomous hypothesis test could be performed
with either a CI or a p value. The 100 (1 - \alpha)% confidence
interval contains all of the parameter values for which p > \alpha
for the current data and model. For example, a 95% confidence interval
contains all of the values for which p > .05.
Note that a confidence interval including 0 does not indicate that the null
(no effect) is true. Rather, it suggests that the observed data together with
the model and its assumptions combined do not provided clear evidence against
a parameter value of 0 (same as with any other value in the interval), with
the level of this evidence defined by the chosen \alpha level (Rafi &
Greenland, 2020; Schweder & Hjort, 2016; Xie & Singh, 2013). To infer no
effect, additional judgments about what parameter values are "close enough"
to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser,
1996).
Plotting with see
The see package contains relevant plotting functions. See the plotting vignette in the see package.
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.
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.
Ben-Shachar, M.S., Patil, I., Thériault, R., Wiernik, B.M., Lüdecke, D. (2023). Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi‑Squared Statistic. Mathematics, 11, 1982. doi:10.3390/math11091982
Bergsma, W. (2013). A bias-correction for Cramer's V and Tschuprow's T. Journal of the Korean Statistical Society, 42(3), 323-328.
Johnston, J. E., Berry, K. J., & Mielke Jr, P. W. (2006). Measures of effect size for chi-squared and likelihood-ratio goodness-of-fit tests. Perceptual and motor skills, 103(2), 412-414.
Rosenberg, M. S. (2010). A generalized formula for converting chi-square tests to effect sizes for meta-analysis. PloS one, 5(4), e10059.
See Also
phi() for more details.
Other effect size from test statistic:
F_to_eta2(),
t_to_d()
Examples
data("Music_preferences")
# chisq.test(Music_preferences)
#>
#> Pearson's Chi-squared test
#>
#> data: Music_preferences
#> X-squared = 95.508, df = 6, p-value < 2.2e-16
#>
chisq_to_cohens_w(95.508,
n = sum(Music_preferences),
nrow = nrow(Music_preferences),
ncol = ncol(Music_preferences)
)
data("Smoking_FASD")
# chisq.test(Smoking_FASD, p = c(0.015, 0.010, 0.975))
#>
#> Chi-squared test for given probabilities
#>
#> data: Smoking_FASD
#> X-squared = 7.8521, df = 2, p-value = 0.01972
chisq_to_fei(
7.8521,
n = sum(Smoking_FASD),
nrow = 1,
ncol = 3,
p = c(0.015, 0.010, 0.975)
)