r_correl: r to Coefficient of Determination (R^2) from F

In MOTE: Effect Size and Confidence Interval Calculator

r to Coefficient of Determination (R^2) from F

Description

This function displays the transformation from r to R^2 to calculate the non-central confidence interval for R^2 using the F distribution.

Usage

r_correl(r, n, a = 0.05)

r.correl(r, n, a = 0.05)

Arguments

r	correlation coefficient
n	sample size
a	significance level

Details

The t-statistic is calculated by:

t = \frac{r}{\sqrt{\frac{1 - r^2}{n - 2}}}

The F-statistic is the t-statistic squared:

F = t^2

Learn more on our example page.

**Note on function and output names:** This effect size is now implemented with the snake_case function name 'r_correl()' to follow modern R style guidelines. The original dotted version 'r.correl()' is still available as a wrapper for backward compatibility, and both functions return the same list. The returned object includes both the original element names (e.g., 'r', 'rlow', 'rhigh', 'R2', 'R2low', 'R2high', 'se', 'n', 'dfm', 'dfe', 't', 'F', 'p', 'estimate', 'estimateR2', 'statistic') and newer snake_case aliases (e.g., 'r_value', 'r_lower_limit', 'r_upper_limit', 'r2_value', 'r2_lower_limit', 'r2_upper_limit', 'standard_error', 'sample_size', 'df_model', 'df_error', 't_value', 'f_value', 'p_value'). New code should prefer 'r_correl()' and the snake_case output names, but existing code using the older names will continue to work.

Value

r

correlation coefficient

rlow

lower level confidence interval for r

rhigh

upper level confidence interval for r

R2

coefficient of determination

R2low

lower level confidence interval of R^2

R2high

upper level confidence interval of R^2

se

standard error

n

sample size

dfm

degrees of freedom of mean

dfe

degrees of freedom of error

t

t-statistic

F

F-statistic

p

p-value

estimate

the r statistic and confidence interval in APA style for markdown printing

estimateR2

the R^2 statistic and confidence interval in APA style for markdown printing

statistic

the t-statistic in APA style for markdown printing

Examples

# This example is derived from the mtcars dataset provided in R.

# What is the correlation between miles per gallon and car weight?

cor.test(mtcars$mpg, mtcars$wt)

r_correl(r = -0.8676594, n = 32, a = .05)

# Backwards-compatible dotted name (deprecated)
r.correl(r = -0.8676594, n = 32, a = .05)

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.