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updated to match content of readings

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aaronshaw
2019-05-08 19:29:01 -05:00
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r_lectures/w07-R_lecture.Rmd
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@@ -61,13 +61,9 @@ chisq.test(table(iris$Species, iris$Sepal.Width > 3))
The incredibly low p-value means that it is very unlikely that these came from the same distribution and that sepal width differs by species. The incredibly low p-value means that it is very unlikely that these came from the same distribution and that sepal width differs by species.
## BONUS: Using simulation to test hypotheses and calculate "exact" p-values
When the assumptions of $\chi^2$ tests aren't met, we can use simulation to approximate how likely a given result is. The material here comes from the final two sections of Chapter 6 of the *OpenIntro* textbook. The book uses the example of a medical practitioner who has 3 complications out of 62 procedures, while the typical rate is 10%.
## Using Simulation
When the assumptions of Chi-squared tests aren't met, we can use simulation to approximate how likely a given result is.
The book uses the example of a medical practitioner who has 3 complications out of 62 procedures, while the typical rate is 10%.
The null hypothesis is that this practitioner's true rate is also 10%, so we're trying to figure out how rare it would be to have 3 or fewer complications, if the true rate is 10%. The null hypothesis is that this practitioner's true rate is also 10%, so we're trying to figure out how rare it would be to have 3 or fewer complications, if the true rate is 10%.
@@ -84,7 +80,6 @@ simulation <- function(rate = .1, n = 62){
} }
# The replicate function runs a function many times # The replicate function runs a function many times
simulated_complications <- replicate(5000, simulation()) simulated_complications <- replicate(5000, simulation())
``` ```
@@ -92,12 +87,10 @@ simulated_complications <- replicate(5000, simulation())
We can look at our simulated complications We can look at our simulated complications
```{r} ```{r}
hist(simulated_complications) hist(simulated_complications)
``` ```
And determine how many of them are as extreme or more extreme than the value we saw. This is the p-value. And determine how many of them are as extreme or more extreme than the value we saw. This is the "exact" p-value.
```{r} ```{r}
sum(simulated_complications <= 3)/length(simulated_complications) sum(simulated_complications <= 3)/length(simulated_complications)