chisq_to_phi | R Documentation |

`\chi^2`

to `\phi`

and Other Correlation-like Effect SizesConvert 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.

```
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, ...)
```

`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 |

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.

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 `\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.

"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).

`see`

The `see`

package contains relevant plotting functions. See the plotting vignette in the `see`

package.

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. \Sexpr[results=rd]{tools:::Rd_expr_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.

`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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