Discrete Data

There is a different set of tests for looking at the statistical significance of discrete random variables (like counts of proportions), and so there is a different set of functions in R for performing those tests.

Proportion Tests

If you have a data set with several different groups of observations and are measuring the probability of success in each group (or the fraction of some other characteristic), you can use the function prop.test to measure whether the difference between groups is statistically significant. Specifically, prop.test can be used for testing the null hypothesis that the proportions (probabilities of success) in several groups are the same or that they equal certain given values:

prop.test(x, n, p = NULL,
          alternative = c("two.sided", "less", "greater"),
          conf.level = 0.95, correct = TRUE)

As an example, let’s revisit the field goal data. Above, we considered the question “is there a difference in the length of attempts indoors and outdoors?” Now, we’ll ask the question “is the probability of success the same indoors as it is outdoors?”

First, let’s create a new data set containing only good and bad field goals. (We’ll eliminate blocked and aborted attempts; there were only 8 aborted attempts and 24 blocked attempts in 2005, but 787 good attempts and 163 bad (no good) attempts.)

> field.goals.goodbad <- field.goals[field.goals$play.type=="FG good" |
                                     field.goals$play.type=="FG no", ]

Now, let’s create a table of successes and failures by stadium type:

> field.goals.table ...

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