Convert Between Effect Sizes for Contingency Tables Correlations

Enables a conversion between different indices of effect size, such as Cohen's w to פ (Fei), and Cramer's V to Tschuprow's T.

Usage

w_to_fei(w, p)

w_to_v(w, nrow, ncol)

w_to_t(w, nrow, ncol)

w_to_c(w)

fei_to_w(fei, p)

v_to_w(v, nrow, ncol)

t_to_w(t, nrow, ncol)

c_to_w(c)

v_to_t(v, nrow, ncol)

t_to_v(t, nrow, ncol)

Arguments

w, c, v, t, fei

Effect size to be converted

p

Vector of expected values. See stats::chisq.test().

nrow, ncol

The number of rows/columns in the contingency table.

References

• 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

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.

See also

cramers_v() chisq_to_fei()

Other convert between effect sizes: d_to_r(), diff_to_cles, eta2_to_f2(), odds_to_probs(), oddsratio_to_riskratio()

Examples

library(effectsize)

## 2D tables
## ---------
data("Music_preferences2")
Music_preferences2
#>       Pop Rock Jazz Classic
#> Psych 151  130   12       7
#> Econ   77    6  111       4
#> Law     0    4    2     165

cramers_v(Music_preferences2, adjust = FALSE)
#> Cramer's V |       95% CI
#> -------------------------
#> 0.80       | [0.75, 1.00]
#> 
#> - One-sided CIs: upper bound fixed at [1.00].

v_to_t(0.80, 3, 4)
#> [1] 0.7228816

tschuprows_t(Music_preferences2)
#> Tschuprow's T (adj.) |       95% CI
#> -----------------------------------
#> 0.72                 | [0.68, 1.00]
#> 
#> - One-sided CIs: upper bound fixed at [1.00].



## Goodness of fit
## ---------------
data("Smoking_FASD")
Smoking_FASD
#>  FAS PFAS   TD 
#>   17   11  640 

cohens_w(Smoking_FASD, p = c(0.015, 0.010, 0.975))
#> Cohen's w |       95% CI
#> ------------------------
#> 0.11      | [0.03, 9.95]
#> 
#> - One-sided CIs: upper bound fixed at [9.95~].

w_to_fei(0.11, p = c(0.015, 0.010, 0.975))
#> [1] 0.01105542

fei(Smoking_FASD, p = c(0.015, 0.010, 0.975))
#> Fei  |       95% CI
#> -------------------
#> 0.01 | [0.00, 1.00]
#> 
#> - Adjusted for uniform expected probabilities.
#> - One-sided CIs: upper bound fixed at [1.00].

## Power analysis
## --------------
# See https://osf.io/cg64s/

p0 <- c(0.35, 0.65)
Fei <- 0.3

pwr::pwr.chisq.test(
  w = fei_to_w(Fei, p = p0),
  df = length(p0) - 1,
  sig.level = 0.01,
  power = 0.85
)
#> 
#>      Chi squared power calculation 
#> 
#>               w = 0.4088311
#>               N = 78.0676
#>              df = 1
#>       sig.level = 0.01
#>           power = 0.85
#> 
#> NOTE: N is the number of observations
#>