userfriendlyscience (version 0.7.2)

# RsqDist: The distribution of R squared (as obtained in a regression analysis)

## Description

These functions use the beta distribution to provide the R Squared distribution.

## Usage

```dRsq(x, nPredictors, sampleSize, populationRsq = 0)
pRsq(q, nPredictors, sampleSize, populationRsq = 0, lower.tail = TRUE)
qRsq(p, nPredictors, sampleSize, populationRsq = 0, lower.tail = TRUE)
rRsq(n, nPredictors, sampleSize, populationRsq = 0)```

## Arguments

x, q

Vector of quantiles, or, in other words, the value(s) of R Squared.

p

Vector of probabilites (p-values).

nPredictors

The number of predictors.

sampleSize

The sample size.

n

The number of R Squared values to generate.

populationRsq

The value of R Squared in the population; this determines the center of the R Squared distribution. This has not been implemented yet in this version of `userfriendlyscience`. If anybody knows how to do this and lets me know, I'll happily integrate this of course.

lower.tail

logical; if TRUE (default), probabilities are the likelihood of finding an R Squared smaller than the specified value; otherwise, the likelihood of finding an R Squared larger than the specified value.

## Value

`dRsq` gives the density, `pRsq` gives the distribution function, `qRsq` gives the quantile function, and `rRsq` generates random deviates.

## Details

The functions use `convert.omegasq.to.f` and `convert.f.to.omegasq` to provide the Omega Squared distribution.

`dbeta`, `pbeta`, `qbeta`, `rbeta`

## Examples

```# NOT RUN {
### Generate 10 random R Squared values
### with 2 predictors and 100 participants
rRsq(10, 2, 100);

### Probability of finding an R Squared of
### .15 with 4 predictors and 100 participants
pRsq(.15, 4, 100, lower.tail = FALSE);

### Probability of finding an R Squared of
### .15 with 15 predictors and 100 participants
pRsq(.15, 15, 100, lower.tail=FALSE);

# }
```