effectsize (version 0.2.0)

t_to_d: Convert test statistics (t, z, F) to effect sizes of differences (Cohen's d) or association (partial r)

Description

These functions are convenience functions to convert t, z and F test statistics to Cohen's d and partial r. These are useful in cases where the data required to compute these are not easily available or their computation is not straightforward (e.g., in liner mixed models, contrasts, etc.).

Usage

t_to_d(t, df_error, pooled = FALSE, ...)
convert_t_to_d(t, df_error, pooled = FALSE, ...)
z_to_d(z, n, ...)
convert_z_to_d(z, n, ...)
F_to_d(f, df, df_error, pooled = FALSE, ...)
convert_F_to_d(f, df, df_error, pooled = FALSE, ...)
t_to_r(t, n = NULL, df_error = NULL, ...)
r_to_t(r, n = NULL, df_error = NULL, ...)
z_to_r(z, n = NULL, df_error = NULL, ...)
r_to_z(r, n = NULL, df_error = NULL, ...)
F_to_r(f, df, df_error = NULL, n = NULL, ...)
convert_t_to_r(t, n = NULL, df_error = NULL, ...)
convert_r_to_t(r, n = NULL, df_error = NULL, ...)
convert_z_to_r(z, n = NULL, df_error = NULL, ...)
convert_r_to_z(r, n = NULL, df_error = NULL, ...)
convert_F_to_r(f, df, df_error = NULL, n = NULL, ...)

Arguments

t, f, z

The t, the F or the z statistics.

pooled

Should the estimate accout for the t-value being based on a repeated-measures design, or not (default).

...

Arguments passed to or from other methods.

n

The number of observations (the sample size).

df, df_error

Degrees of freedom of numerator or of the error estimate (i.e., the residuals).

r

The correlation coefficient r.

Value

A numeric value of the requested effect size.

Details

These functions use the following formulae:

$$r_{partial} = t / \sqrt{t^2 + df_{error}}$$

$$r_{partial} = z / \sqrt{z^2 + N}$$

$$Cohen's d = 2 * t / \sqrt{df_{error}}$$

$$Cohen's d_z = t / \sqrt{df_{error}}$$

$$Cohen's d = 2 * z / \sqrt{N}$$

References

• Friedman, H. (1982). Simplified determinations of statistical power, magnitude of effect and research sample sizes. Educational and Psychological Measurement, 42(2), 521-526. 10.1177/001316448204200214

• Wolf, F. M. (1986). Meta-analysis: Quantitative methods for research synthesis (Vol. 59). Sage.

• Rosenthal, R. (1991). Meta-analytic procedures for social research. Newbury Park, CA: SAGE Publications, Incorporated.

Examples

# NOT RUN {
## t Tests
res <- t.test(1:10, y = c(7:20), var.equal = TRUE)
t_to_d(t = res$statistic, res$parameter)
t_to_r(t = res$statistic, res$parameter)

res <- with(sleep, t.test(extra[group == 1], extra[group == 2], paired = TRUE))
t_to_d(t = res$statistic, res$parameter, pooled = TRUE)
t_to_r(t = res$statistic, res$parameter)

res <- cor.test(iris$Sepal.Width, iris$Petal.Width)
t_to_r(t = res$statistic, n = 150)

# }
# NOT RUN {
## Linear Regression
model <- lm(Sepal.Length ~ Sepal.Width + Petal.Length, data = iris)
library(parameters)
(param_tab <- parameters(model))
# > Parameter    | Coefficient |   SE |       95% CI |     t |  df |      p
# > -----------------------------------------------------------------------
# > (Intercept)  |        2.25 | 0.25 | [1.76, 2.74] |  9.07 | 147 | < .001
# > Sepal.Width  |        0.60 | 0.07 | [0.46, 0.73] |  8.59 | 147 | < .001
# > Petal.Length |        0.47 | 0.02 | [0.44, 0.51] | 27.57 | 147 | < .001

t_to_r(param_tab$t[2:3], param_tab$df_error[2:3])
# > [1] 0.5781005 0.9153894
# }
# NOT RUN {
# How does this compare to actual partial correlations?
if (require("ppcor")) {
  pcor(iris[1:3])$estimate[1, -1]
}
# }