Comparing Distributions |
We have already considered several methods that help us study the distribution of a sample of data, including histograms and stem plots. These may also be used to compare the features of two or more distributions. Howver, there are other graphical tools that are often better for making comparisons between samples.
Simultaneous boxplots are often useful for comparing the location and spread of several datasets. Sometimes we have a more sharply focussed question: does our sample appear to from a particular theoretical distribution such as the normal, or do two samples seem to have the same distribution? For the latter type of question superimposed density plots and quantile-quantile plots are often more useful. Quantile-quantile plots (plotting the two sets of sorted data against each other) are in some sense a direct comparison of two cumulative distribution functions.