# d.to.r: r and Coefficient of Determination (R2) from d In MOTE: Effect Size and Confidence Interval Calculator

## Description

Calculates r from d and then translates r to r2 to calculate the non-central confidence interval for r2 using the F distribution.

## Usage

 `1` ```d.to.r(d, n1, n2, a = 0.05) ```

## Arguments

 `d` effect size statistic `n1` sample size group one `n2` sample size group two `a` significance level

## Details

The correlation coefficient (r) is calculated by dividing Cohen's d by the square root of the total sample size squared - divided by the product of the sample sizes of group one and group two.

r = d / sqrt(d^2 + (n1 + n2)^2 / (n1*n2))

## Value

Provides the effect size (correlation coefficient) with associated confidence intervals, the t-statistic, F-statistic, and other estimates appropriate for d to r translation. Note this CI is not based on the traditional r-to-z transformation but rather non-central F using the ci.R function from MBESS.

 `r` correlation coefficient `rlow` lower level confidence interval r `rhigh` upper level confidence interval r `R2` coefficient of determination `R2low` lower level confidence interval of R2 `R2high` upper level confidence interval of R2 `se` standard error `n` sample size `dfm` degrees of freedom of mean `dfe` degrees of freedom 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37``` ```#The following example is derived from the "indt_data" dataset, included #in the MOTE library. #A forensic psychologist conducted a study to examine whether #being hypnotized during recall affects how well a witness #can remember facts about an event. Eight participants #watched a short film of a mock robbery, after which #each participant was questioned about what he or she had #seen. The four participants in the experimental group #were questioned while they were hypnotized. The four #participants in the control group recieved the same #questioning without hypnosis. t.test(correctq ~ group, data = indt_data) #You can type in the numbers directly, or refer to the dataset, #as shown below. d.ind.t(m1 = 17.75, m2 = 23, sd1 = 3.30, sd2 = 2.16, n1 = 4, n2 = 4, a = .05) d.ind.t(17.75, 23, 3.30, 2.16, 4, 4, .05) d.ind.t(mean(indt_data\$correctq[indt_data\$group == 1]), mean(indt_data\$correctq[indt_data\$group == 2]), sd(indt_data\$correctq[indt_data\$group == 1]), sd(indt_data\$correctq[indt_data\$group == 2]), length(indt_data\$correctq[indt_data\$group == 1]), length(indt_data\$correctq[indt_data\$group == 2]), .05) #Contrary to the hypothesized result, the group that underwent #hypnosis were significantly less accurate while reporting #facts than the control group with a large effect size, t(6) = -2.66, #p = .038, d_s = 1.88. d.to.r(d = -1.88, n1 = 4, n2 = 4, a = .05) ```

MOTE documentation built on May 2, 2019, 5:51 a.m.