Skewness and kurtosis values in descriptives

Jana · May 2016

Hi all,

I already posted this on Twitter but was referred to the forum, so I'll bring it up here again I recently started using JASP but tend to doublecheck relevant values in R. Today I calculated simple descriptives for my data. In R, I am using the library pastecs, and the values for skewness and kurtosis (as well as the SEs, obviously) differ from those provided in JASP. The general direction is the same (i.e., I have one non-normally distributed variable with high skew and kurtosis), but the numeric values differ quite a bit. All other values are identical though. Any ideas why that might be? Because I am unsure which ones to report now.

Thanks in advance!

RaviSelker · May 2016

This is how we calculate skewness and kurtosis:

.descriptivesKurtosis <- function(x) {

    # Kurtosis function as in SPSS: 
    # http://www.ats.ucla.edu/stat/mult_pkg/faq/general/kurtosis.htm
    # http://en.wikipedia.org/wiki/Kurtosis#Estimators_of_population_kurtosis

    n <- length(x)
    s4 <- sum((x - mean(x))^4)
    s2 <- sum((x - mean(x))^2)
    v <- s2 / (n-1)
    a <- (n * (n + 1)) / ((n - 1) * (n - 2) * (n - 3))
    b <- s4 / (v^2)
    c <- (-3 * (n - 1)^2) / ((n - 2) * (n - 3))
    kurtosis <- a * b + c
    return(kurtosis)
}

.descriptivesSkewness <- function(x) {

    # Skewness function as in SPSS (for samples spaces): 
    # http://suite101.com/article/skew-and-how-skewness-is-calculated-in-statistical-software-a231005

    n <- length(x)
    m <- mean(x)
    s <- sd(x) 
    z <- (x - m) / s  # z scores
    a <- n / ((n - 1) * (n - 2))
    skewness <- sum(z^3) * a
    return(skewness)
}

I'm not sure how the R package calculates these statistics. Could you attach the csv you are using to calculate these statistics so I can check it?

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