effectsize (version 0.4.0)

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.).

See Effect Size from Test Statistics vignette.

Usage

t_to_d(t, df_error, paired = FALSE, ci = 0.95, pooled, ...)
z_to_d(z, n, paired = FALSE, ci = 0.95, pooled, ...)
F_to_d(f, df, df_error, paired = FALSE, ci = 0.95, pooled, ...)
t_to_r(t, df_error, ci = 0.95, ...)
z_to_r(z, n, ci = 0.95, ...)
F_to_r(f, df, df_error, ci = 0.95, ...)

Arguments

t, f, z

The t, the F or the z statistics.

paired

Should the estimate accout for the t-value being testing the difference between dependant means?

ci

Confidence Interval (CI) level

pooled

Deprecated. Use paired.

...

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).

Value

A data frame with the effect size(s) between 0-1, and confidence interval(s)

Details

These functions use the following formulae to approximate r and d:

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

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

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

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

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

Confidence Intervals

Confidence intervals are estimated using the Noncentrality parameter method; These methods searches for a the best ncp (non-central parameters) for of the noncentral F distribution for the desired tail-probabilities, and then convert these ncps to the corresponding effect sizes.

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.

• Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182.

• 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.

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, paired = TRUE)
t_to_r(t = res$statistic, res$parameter)

# }
# NOT RUN {
## Linear Regression
model <- lm(Sepal.Length ~ Sepal.Width + Petal.Length, data = iris)
library(parameters)
(param_tab <- parameters(model))

(rs <- t_to_r(param_tab$t[2:3], param_tab$df_error[2:3]))

if(require(see)) plot(rs)

# How does this compare to actual partial correlations?
if (require("correlation")) {
  correlation::correlation(iris[,1:3], partial = TRUE)[1:2, c(2,3,7,8)]
}

## Use with emmeans based contrasts (see also t_to_eta2)
if (require(emmeans)) {
  warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)

  conts <- summary(pairs(emmeans(warp.lm,  ~ tension | wool)))
  t_to_d(conts$t.ratio, conts$df)
}

# }
# NOT RUN {
# }