# tukeyCount: Results of a Simulation to Tukey's Fast Test In MSG: Data and Functions for the Book Modern Statistical Graphics

## 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.

## Source

Simulation; see the Examples section below.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36``` ```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") } ```

MSG documentation built on May 29, 2017, 4:30 p.m.