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# 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: ...

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