zscore(q, distribution, ...)
zscoreGamma(q, shape, rate = 1, scale = 1/rate)
zscoreT(x, df, approx=FALSE)
tZscore(x, df)
zscoreHyper(q, m, n, k)zscoreT or >=1 for tZscore)TRUE then a fast approximation is used to convert t-statistics into z-scores. If FALSE, z-scores will be exact.qhyperqhyperqhypertZscore which gives deviates from the specified t-distribution.
z <- zscoreT(x,df=df) then pnorm(z) equals pt(x,df=df).zscore works for any distribution for which a cumulative distribution function (like pnorm) exists in R.
The argument distribution is the name of the cumulative distribution function with the "p" removed.
zscoreGamma, zscoreT and zscoreHyper are specific functions for the gamma, t and hypergeometric distributions respectively.
tZscore is the inverse of zscoreT, and computes t-distribution equivalents for standard normal deviates.
The transformation to z-scores is done by converting to log tail probabilities, and then using qnorm.
For numerical accuracy, the left or right tail is used, depending on which is likely to be smaller.
If approx=TRUE, then the approximation from Hill (1970) is used to convert t-statistics to z-scores directly without computing tail probabilities.
Brophy (1987) showed this to be most accurate of a variety of possible closed-form transformations.
Brophy, AL (1987). Efficient estimation of probabilities in the t distribution. Behavior Research Methods 19, 462--466.
qnorm, pgamma, pt in the stats package.
# First three are equivalent
zscore(c(1,2.5), dist="gamma", shape=0.5, scale=2)
zscore(c(1,2.5), dist="chisq", df=1)
zscoreGamma(c(1,2.5), shape=0.5, scale=2)
zscoreT(2, df=3)
tZscore(2, df=3)
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