MSG (version 0.8)

tukeyCount: Results of a Simulation to Tukey's Fast Test

Description

For the test of means of two samples, we calculated the P-values and recorded the counts of Tukey's rule of thumb.

Format

A data frame with 10000 observations on the following 3 variables.

pvalue.t

P-values of t test

pvalue.w

P-values of Wilcoxon test

count

Tukey's counts

Details

See the reference for details.

References

D. Daryl Basler and Robert B. Smawley. Tukey's Compact versus Classic Tests. The Journal of Experimental Education, Vol. 36, No. 3 (Spring, 1968), pp. 86-88

Examples

# NOT RUN {
data(tukeyCount)

## does Tukey's rule of thumb agree with t test and Wilcoxon test?
with(tukeyCount, {
    ucount = unique(count)
    stripchart(pvalue.t ~ count, method = "jitter", jitter = 0.2, pch = 19,
        cex = 0.7, vertical = TRUE, at = ucount - 0.2, col = rgb(1, 0, 0, 0.2),
        xlim = c(min(count) - 1, max(count) + 1), xaxt = "n", xlab = "Tukey Count",
        ylab = "P-values")
    stripchart(pvalue.w ~ count, method = "jitter", jitter = 0.2, pch = 21,
        cex = 0.7, vertical = TRUE, at = ucount + 0.2, add = TRUE, col = rgb(0,
            0, 1, 0.2), xaxt = "n")
    axis(1, unique(count))
    lines(sort(ucount), tapply(pvalue.t, count, median), type = "o", pch = 19,
        cex = 1.3, col = "red")
    lines(sort(ucount), tapply(pvalue.w, count, median), type = "o", pch = 21,
        cex = 1.3, col = "blue", lty = 2)
    legend("topright", c("t test", "Wilcoxon test"), col = c("red", "blue"),
        pch = c(19, 21), lty = 1:2, bty = "n", cex = 0.8)
})

if (interactive()) {

    ## this is how the data was generated
    set.seed(402)
    n = 30
    tukeyCount = data.frame(t(replicate(10000, {
        x1 = rweibull(n, runif(1, 0.5, 4))
        x2 = rweibull(n, runif(1, 1, 5))
        c(t.test(x1, x2)$p.value, wilcox.test(x1, x2)$p.value, with(rle(rep(0:1,
            each = n)[order(c(x1, x2))]), ifelse(head(values, 1) == tail(values,
            1), 0, sum(lengths[c(1, length(lengths))]))))
    })))
    colnames(tukeyCount) = c("pvalue.t", "pvalue.w", "count")

}
# }