## Section 4.1 examples

# P-value:

pchisq(test.stat, df=2, lower=F)

### Example 1:  tree data:

## Testing for a difference between p_1 and p_2:

# We can specify the number of successes and the sample sizes for each sample:

prop.test(c(64,89), n=c(160,261), alternative="two.sided", correct=FALSE)

# Or we can equivalently specify the number of successes and 
# number of failures for each sample:

prop.test(matrix(c(64,96,89,172),nrow=2,ncol=2,byrow=TRUE), alternative="two.sided", correct=FALSE)


### Example 2:  lighting data:


prop.test(matrix(c(714,111,662,154),nrow=2,ncol=2,byrow=TRUE), alternative="greater", correct=FALSE)


### Example 3:  bank jobs data:


fisher.test(matrix(c(1,9,3,1),nrow=2,ncol=2,byrow=TRUE), alternative="less")


### Example 4:  cancer drug study example:

## Enter each 2-by-2 table, separately, by columns:

cancer.data <-
array(c(10, 12, 1, 1,
        9, 11, 0, 1,
        8, 7, 0, 3),
      dim = c(2, 2, 3),
      dimnames = list(
          Drug = c("Treatment", "Control"),
          Response = c("Success", "Failure"),
          Group = c("1", "2", "3")))

print(cancer.data)

## Mantel-Haenszel test

mantelhaen.test(cancer.data, alternative="greater")

## This p-value is based on T4 with a continuity correction