chisq_to_phi | R Documentation |

Convert between *χ^2* (chi-square), *φ* (phi), Cramer's
*V*, Tschuprow's *T*, Cohen's *w*,
פ (Fei) and Pearson's *C* for contingency
tables or goodness of fit.

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, 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, ...)

`chisq` |
The |

`n` |
Total sample size. |

`nrow, ncol` |
The number of rows/columns in the contingency table. |

`adjust` |
Should the effect size be bias-corrected? 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 |

These functions use the following formulas:

*phi = w = sqrt(\frac{χ^2}{n})*

*Cramer's V = φ / sqrt(min(nrow, ncol) - 1)*

*Tschuprow's T = φ / sqrt(sqrt((nrow-1) * (ncol-1)))*

*פ = w / sqrt(1 / min(p_E) - 1))*

Where *p_E* are the expected probabilities.

*Pearson's C = sqrt(χ^2 / (χ^2 + n))*

For bias-adjusted versions of *φ* and *V*, see Bergsma, 2013.

A data frame with the effect size(s), and confidence interval(s). See
`cramers_v()`

.

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 *χ^2* distribution that places the observed
*t*, *F*, or *χ^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.

"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 - *α*)% confidence
interval contains all of the parameter values for which *p* > *α*
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 *α* 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).

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.

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.

`phi()`

for more details.

Other effect size from test statistic:
`F_to_eta2()`

,
`t_to_d()`

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) )

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