# R Dataset / Package HistData / ZeaMays

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On this Picostat.com statistics page, you will find information about the ZeaMays data set which pertains to Darwin's Heights of Cross- and Self-fertilized Zea May Pairs. The ZeaMays data set is found in the HistData R package. You can load the ZeaMays data set in R by issuing the following command at the console data("ZeaMays"). This will load the data into a variable called ZeaMays. If R says the ZeaMays data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the ZeaMays R data set. The size of this file is about 350 bytes. ## Darwin's Heights of Cross- and Self-fertilized Zea May Pairs## DescriptionDarwin (1876) studied the growth of pairs of zea may (aka corn) seedlings, one produced by cross-fertilization and the other produced by self-fertilization, but otherwise grown under identical conditions. His goal was to demonstrate the greater vigour of the cross-fertilized plants. The data recorded are the final height (inches, to the nearest 1/8th) of the plants in each pair. In the ## Usagedata(ZeaMays) ## FormatA data frame with 15 observations on the following 4 variables. `pair` pair number, a numeric vector `pot` pot, a factor with levels `1` `2` `3` `4` `cross` height of cross fertilized plant, a numeric vector `self` height of self fertilized plant, a numeric vector `diff` `cross - self` for each pair
## DetailsIn addition to the standard paired t-test, several types of non-parametric tests can be contemplated: (a) Permutation test, where the values of, say (b) Permutation test based on assigning each (c) Wilcoxon signed rank test: tests the hypothesis that the median signed rank of the ## SourceDarwin, C. (1876). Andrews, D. and Herzberg, A. (1985) ## ReferencesFisher, R. A. (1935). ## See Also
## Examplesdata(ZeaMays)################################## ## Some preliminary exploration ## ################################## boxplot(ZeaMays[,c("cross", "self")], ylab="Height (in)", xlab="Fertilization")# examine large individual diff/ces largediff <- subset(ZeaMays, abs(diff) > 2*sd(abs(diff))) with(largediff, segments(1, cross, 2, self, col="red"))# plot cross vs. self. NB: unusual trend and some unusual points with(ZeaMays, plot(self, cross, pch=16, cex=1.5)) abline(lm(cross ~ self, data=ZeaMays), col="red", lwd=2)# pot effects ? anova(lm(diff ~ pot, data=ZeaMays))############################## ## Tests of mean difference ## ############################## # Wilcoxon signed rank test # signed ranks: with(ZeaMays, sign(diff) * rank(abs(diff))) wilcox.test(ZeaMays$cross, ZeaMays$self, conf.int=TRUE, exact=FALSE)# t-tests with(ZeaMays, t.test(cross, self)) with(ZeaMays, t.test(diff))mean(ZeaMays$diff) # complete permutation distribution of diff, for all 2^15 ways of assigning # one value to cross and the other to self (thx: Bert Gunter) N <- nrow(ZeaMays) allmeans <- as.matrix(expand.grid(as.data.frame( matrix(rep(c(-1,1),N), nr =2)))) %*% abs(ZeaMays$diff) / N# upper-tail p-value sum(allmeans > mean(ZeaMays$diff)) / 2^N # two-tailed p-value sum(abs(allmeans) > mean(ZeaMays$diff)) / 2^Nhist(allmeans, breaks=64, xlab="Mean difference, cross-self", main="Histogram of all mean differences") abline(v=c(1, -1)*mean(ZeaMays$diff), col="red", lwd=2, lty=1:2)plot(density(allmeans), xlab="Mean difference, cross-self", main="Density plot of all mean differences") abline(v=c(1, -1)*mean(ZeaMays$diff), col="red", lwd=2, lty=1:2) -- Dataset imported from https://www.r-project.org. |

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Attachment | Size |
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dataset-75564.csv | 350 bytes |