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

Description Usage Arguments Details Value Examples

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

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

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

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))

Learn more on our example page.

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

#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)