R - Chi Square Test

Chi-Square test is a statistical method to determine if two categorical variables have a significant correlation between them. Both those variables should be from same population and they should be categorical like − Yes/No, Male/Female, Red/Green etc.

For example, we can build a data set with observations on people's ice-cream buying pattern and try to correlate the gender of a person with the flavor of the ice-cream they prefer. If a correlation is found we can plan for appropriate stock of flavors by knowing the number of gender of people visiting.

Syntax

The function used for performing chi-Square test is chisq.test().

The basic syntax for creating a chi-square test in R is −

chisq.test(data)

Following is the description of the parameters used −

• data is the data in form of a table containing the count value of the variables in the observation.

Example

We will take the Cars93 data in the "MASS" library which represents the sales of different models of car in the year 1993.

library("MASS")
print(str(Cars93))

When we execute the above code, it produces the following result −

'data.frame':   93 obs. of  27 variables: 
 $ Manufacturer      : Factor w/ 32 levels "Acura","Audi",..: 1 1 2 2 3 4 4 4 4 5 ... 
 $ Model             : Factor w/ 93 levels "100","190E","240",..: 49 56 9 1 6 24 54 74 73 35 ... 
 $ Type              : Factor w/ 6 levels "Compact","Large",..: 4 3 1 3 3 3 2 2 3 2 ... 
 $ Min.Price         : num  12.9 29.2 25.9 30.8 23.7 14.2 19.9 22.6 26.3 33 ... 
 $ Price             : num  15.9 33.9 29.1 37.7 30 15.7 20.8 23.7 26.3 34.7 ... 
 $ Max.Price         : num  18.8 38.7 32.3 44.6 36.2 17.3 21.7 24.9 26.3 36.3 ... 
 $ MPG.city          : int  25 18 20 19 22 22 19 16 19 16 ... 
 $ MPG.highway       : int  31 25 26 26 30 31 28 25 27 25 ... 
 $ AirBags           : Factor w/ 3 levels "Driver & Passenger",..: 3 1 2 1 2 2 2 2 2 2 ... 
 $ DriveTrain        : Factor w/ 3 levels "4WD","Front",..: 2 2 2 2 3 2 2 3 2 2 ... 
 $ Cylinders         : Factor w/ 6 levels "3","4","5","6",..: 2 4 4 4 2 2 4 4 4 5 ... 
 $ EngineSize        : num  1.8 3.2 2.8 2.8 3.5 2.2 3.8 5.7 3.8 4.9 ... 
 $ Horsepower        : int  140 200 172 172 208 110 170 180 170 200 ... 
 $ RPM               : int  6300 5500 5500 5500 5700 5200 4800 4000 4800 4100 ... 
 $ Rev.per.mile      : int  2890 2335 2280 2535 2545 2565 1570 1320 1690 1510 ... 
 $ Man.trans.avail   : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 1 1 1 1 ... 
 $ Fuel.tank.capacity: num  13.2 18 16.9 21.1 21.1 16.4 18 23 18.8 18 ... 
 $ Passengers        : int  5 5 5 6 4 6 6 6 5 6 ... 
 $ Length            : int  177 195 180 193 186 189 200 216 198 206 ... 
 $ Wheelbase         : int  102 115 102 106 109 105 111 116 108 114 ... 
 $ Width             : int  68 71 67 70 69 69 74 78 73 73 ... 
 $ Turn.circle       : int  37 38 37 37 39 41 42 45 41 43 ... 
 $ Rear.seat.room    : num  26.5 30 28 31 27 28 30.5 30.5 26.5 35 ... 
 $ Luggage.room      : int  11 15 14 17 13 16 17 21 14 18 ... 
 $ Weight            : int  2705 3560 3375 3405 3640 2880 3470 4105 3495 3620 ... 
 $ Origin            : Factor w/ 2 levels "USA","non-USA": 2 2 2 2 2 1 1 1 1 1 ... 
 $ Make              : Factor w/ 93 levels "Acura Integra",..: 1 2 4 3 5 6 7 9 8 10 ... 

The above result shows the dataset has many Factor variables which can be considered as categorical variables. For our model we will consider the variables "AirBags" and "Type". Here we aim to find out any significant correlation between the types of car sold and the type of Air bags it has. If correlation is observed we can estimate which types of cars can sell better with what types of air bags.

# Load the library.
library("MASS")

# Create a data frame from the main data set.
car.data <- data.frame(Cars93$AirBags, Cars93$Type)

# Create a table with the needed variables.
car.data = table(Cars93$AirBags, Cars93$Type) 
print(car.data)

# Perform the Chi-Square test.
print(chisq.test(car.data))

When we execute the above code, it produces the following result −

                     Compact Large Midsize Small Sporty Van
  Driver & Passenger       2     4       7     0      3   0
  Driver only              9     7      11     5      8   3
  None                     5     0       4    16      3   6

         Pearson's Chi-squared test

data:  car.data
X-squared = 33.001, df = 10, p-value = 0.0002723

Warning message:
In chisq.test(car.data) : Chi-squared approximation may be incorrect

Conclusion

The trend in the above graph helps us predicting the probability of survival at the end of a certain number of days.