Convert effect sizes to a common metric (Pearson's r)

Converts a variety of effect sizes and test statistics to Pearson's r for comparability. Effect sizes that cannot be meaningfully converted are returned as NA with appropriate warnings.

Usage

convert_effect_sizes(es_values, es_types, quiet = FALSE)

Arguments

es_values: Numeric vector of effect sizes, or character vector for test statistics formatted in APA style (e.g., "t(10) = 2.5").
es_types: Character vector of effect size types (case-insensitive). See Details for accepted values. Unrecognized types trigger a warning.
quiet: Logical. If TRUE, suppresses warnings about unknown effect size types and messages about non-convertible or missing values.

Value

Numeric vector of effect sizes converted to Pearson's r. Returns NA for values that cannot be converted or are missing.

Details

Supported Effect Sizes

The following effect sizes can be converted to r. Accepted es_types values are case-insensitive.

Pearson's r / phi: "r", "phi", "φ"
Conversion: Returned as-is.
Sign: Preserved.
R-squared: "r2", "r^2", "r²", "r-square"
Conversion: \(r = \sqrt{R^2}\)
Sign: Always positive (R² is non-directional).
Cohen's d / Hedges' g: "d", "cohen's d", "hedges' g", "smd"
Conversion: \(r = \frac{d}{\sqrt{d^2 + 4}}\)
Sign: Preserved (if input d is negative, r is negative).
Odds ratio: "or", "odds ratio"
Conversion: \(d = \ln(OR) \cdot \sqrt{3} / \pi\), then d to r.
Sign: Preserved (OR < 1 implies negative r).
Eta-squared: "etasq", "eta^2", "η²"
Conversion: \(d = 2\sqrt{\frac{\eta^2}{1 - \eta^2}}\), then d to r.
Sign: Always positive.
Cohen's f / f²: "f", "cohen's f", "f2", "f^2", "f²"
Conversion (f): \(d = 2f\), then d to r.
Conversion (f²): \(R^2 = \frac{f^2}{1 + f^2}\), then \(r = \sqrt{R^2}\).
Sign: Always positive.

Test Statistics

When es_types is "test statistic" the function parses APA-formatted strings in es_values.

t-test: Format: "t(df) = value"
Conversion: \(r = \frac{t}{\sqrt{t^2 + df}}\)
Sign: Preserved.
F-test: Format: "F(df1, df2) = value"
Constraint: df1 must equal 1.
Conversion: \(t = \sqrt{F}\), then t to r.
Sign: Always positive.
z-test: Format: "z = value, N = value"
Conversion: \(r = \frac{z}{\sqrt{z^2 + N}}\)
Sign: Preserved.
Chi-squared: Format: "x2(1, N = value) = value"
Constraint: df must equal 1.
Conversion: \(r = \sqrt{\frac{\chi^2}{N}}\)
Sign: Always positive.

Non-Convertible Effect Sizes

The following effect sizes cannot be reliably converted to r and return NA: partial eta-squared, Cramer's V, Cohen's h, Cohen's \(d_z\), regression coefficients ("b", "beta"), and semi-partial correlations.

References

Sánchez-Meca, J., Marín-Martínez, F., & Chacón-Moscoso, S. (2003). Effect-size indices for dichotomized outcomes in meta-analysis. Psychological Methods, 8(4), 448–467. doi:10.1037/1082-989X.8.4.448