Homework3.2.R

# Chi-Squared test using Motor Trend Car Road Tests data set.
# Store the data in the variable mydata
mydata2  <- mtcars

# Research Question:Is there an association between vs Vs am, gear Vs carb, gear Vs cylinder?
#H0 = two variables are independent
#H1 = two variables are related

# Generate frequency table. If values in all cells are same, then have a balanced design.
case1 <- table(mydata2$vs, mydata2$am)
case1

##    
##      0  1
##   0 12  6
##   1  7  7

case2 <- table(mydata2$gear, mydata2$carb)
case2

##    
##     1 2 3 4 6 8
##   3 3 4 3 5 0 0
##   4 4 4 0 4 0 0
##   5 0 2 0 1 1 1

case3 <- table(mydata2$cyl, mydata2$gear)
case3

##    
##      3  4  5
##   4  1  8  2
##   6  2  4  1
##   8 12  0  2

#chisquare case1 test
#the p-value > 0.05, then there is a no tilt to the
#stacks (the counts are not likely to be from chance).
chisq.test(case1)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  case1
## X-squared = 0.34754, df = 1, p-value = 0.5555

#chisquare case2 test
#the p-value > 0.05, then there is a no tilt to the
#stacks (the counts are not likely to be from chance).
chisq.test(case2)

## Warning in chisq.test(case2): Chi-squared approximation may be incorrect

## 
##  Pearson's Chi-squared test
## 
## data:  case2
## X-squared = 16.518, df = 10, p-value = 0.08573

#chisquare case3 test
#the p-value < 0.05, then there is a tilt to the
#stacks (the counts are not likely to be from chance).
chisq.test(case3)

## Warning in chisq.test(case3): Chi-squared approximation may be incorrect

## 
##  Pearson's Chi-squared test
## 
## data:  case3
## X-squared = 18.036, df = 4, p-value = 0.001214

#critical value case1
#Chi Square value < Critical Value, fail to reject the null hypothesis that means 
#two variables are independent- Engine(vs) (0 = V-shaped, 1 = straight) is not related to 
#Transmission(am) (0 = automatic, 1 = manual)
qchisq(0.95,1)

## [1] 3.841459

#critical value case2
#Chi Square value < Critical Value, fail to reject the null hypothesis that means 
#two variables are independent, Number of forward gears is not related to Number of carburetors
qchisq(0.95,10)

## [1] 18.30704

#critical value case3
#Chi Square value > Critical Value, reject the null hypothesis that means accepting two variables
#are related, Number of cylinders are related to Number of forward gears
qchisq(0.95,4)

## [1] 9.487729