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How to perform chi square test for goodness of fit in R?
The chi square test for goodness of fit is a nonparametric test to test whether the observed values that falls into two or more categories follows a particular distribution of not. We can say that it compares the observed proportions with the expected chances. In R, we can perform this test by using chisq.test function. Check out the below examples to understand how it is done.
Example1
> x1<-sample(0:9,200,replace=TRUE) > x1
Output
[1] 9 4 1 9 6 6 1 6 0 0 5 8 8 3 7 8 0 3 3 9 6 0 3 8 2 0 8 5 9 1 3 4 6 7 0 1 4 [38] 5 4 8 1 7 2 1 1 3 4 2 5 6 3 4 4 5 6 8 6 4 6 2 0 0 5 2 0 1 6 9 3 0 5 1 3 9 [75] 8 0 9 5 9 4 2 5 9 2 2 0 6 9 1 8 0 1 7 8 4 0 0 2 5 7 1 0 6 7 0 8 8 5 4 3 4 [112] 6 7 4 7 2 1 4 4 4 2 8 4 4 5 6 5 0 5 7 1 5 7 3 4 1 7 9 1 3 9 0 7 1 5 7 7 5 [149] 6 3 4 8 1 8 2 6 8 8 8 8 1 0 9 3 1 6 9 1 5 4 9 3 4 2 6 8 1 6 5 1 0 8 5 0 7 [186] 2 5 8 0 3 6 3 6 7 7 8 4 0 8 3
Example
> x1_table<-table(x1) > x1_table
Output
x1 0 1 2 3 4 5 6 7 8 9 24 23 14 18 23 21 21 17 24 15 > chisq.test(x1_table,p=rep(0.1,10)) Chi-squared test for given probabilities data: x1_table X-squared = 6.3, df = 9, p-value = 0.7096
Example2
> x2<-c(14,25,17,14) > p<-c(0.25,0.25,0.25,0.25) > chisq.test(x2,p=p)
Output
Chi-squared test for given probabilities data: x2 X-squared = 4.6286, df = 3, p-value = 0.2011
Example3
> x3<-rpois(200,5) > x3
Output
[1] 3 2 4 4 5 4 9 5 8 8 2 9 5 0 7 3 3 4 8 4 3 7 3 7 3 [26] 2 4 2 7 5 7 5 2 5 3 6 4 6 4 5 7 7 6 7 5 9 6 6 4 1 [51] 6 4 5 7 8 7 3 3 2 7 3 6 7 7 1 2 1 3 7 6 5 5 3 4 5 [76] 2 5 5 3 5 5 7 5 3 10 8 6 3 6 10 6 3 2 3 3 7 4 6 2 5 [101] 3 5 3 2 4 4 3 4 7 5 6 7 9 4 4 6 4 10 4 2 4 0 4 3 6 [126] 5 5 1 4 5 5 6 6 5 1 7 2 4 6 6 5 2 2 5 7 2 6 5 3 8 [151] 2 5 4 4 4 3 4 4 9 4 7 2 6 2 3 5 5 3 8 5 5 9 4 4 7 [176] 5 6 6 5 6 3 3 8 5 5 9 6 9 8 4 8 3 2 6 6 4 6 6 7 6
Example
> x3_table<-table(x3) > x3_table
Output
x3 0 1 2 3 4 5 6 7 8 9 10 2 5 20 29 33 37 30 23 10 8 3 > chisq.test(x3_table,p=rep(1/11,11)) Chi-squared test for given probabilities data: x3_table X-squared = 93.15, df = 10, p-value = 1.268e-15
Example4
> x4<-c(24,98,30,35,27,28) > chisq.test(x4)
Output
Chi-squared test for given probabilities data: x4 X-squared = 100.6, df = 5, p-value < 2.2e-16
Example5
> x5<-c(12,15,17,15,9,14) > p<-c(0.1,0.1,0.2,0.2,0.1,0.1) > chisq.test(x5,p)
Output
Pearson's Chi-squared test data: x5 and p X-squared = 3.75, df = 4, p-value = 0.4409 Warning message: In chisq.test(x5, p) : Chi-squared approximation may be incorrect
Example6
> x6<-c(36,27,25,84,14,25,36,27,29) > chisq.test(x6,p=rep(1/9,9))
Output
Chi-squared test for given probabilities data: x6 X-squared = 94.812, df = 8, p-value < 2.2e-16
Updated on: 21-Nov-2020
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