updated to match content of readings

r_lectures/w07-R_lecture.Rmd

@@ -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.
 
+## BONUS: Using simulation to test hypotheses and calculate "exact" p-values
 
-
-## 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%.
+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%.
 
 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
-
 simulated_complications <- replicate(5000, simulation())
 
 ```
@@ -92,12 +87,10 @@ simulated_complications <- replicate(5000, simulation())
 We can look at our simulated complications
 
 ```{r}
-
 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}
 
 sum(simulated_complications <= 3)/length(simulated_complications)