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How to identify the difference between Kolmogorov Smirnov test and Chi Square Goodness of fit test in R?
The Chi Square Goodness of fit test is used to test whether the distribution of nominal variables is same or not as well as for other distribution matches and on the other hand the Kolmogorov Smirnov test is only used to test to the goodness of fit for a continuous data. The difference is not about the programming tool, it is a concept of statistics.
Example
> x<-rnorm(20) > x
Output
[1] 0.078716115 -0.682154062 0.655436957 -1.169616157 -0.688543382 [6] 0.646087104 0.472429834 2.277750805 0.963105637 0.414918478 [11] 0.575005958 -1.286604138 -1.026756390 2.692769261 -0.835433410 [16] 0.007544065 0.925296720 1.058978610 0.906392907 0.973050503
Example
> ks.test(x,pnorm) One-sample Kolmogorov-Smirnov test data: x D = 0.2609, p-value = 0.1089 alternative hypothesis: two-sided Chi-Square test: > chisq.test(x,p=rep(1/20,20)) Error in chisq.test(x, p = rep(1/20, 20)) : all entries of 'x' must be nonnegative and finite
With discrete distribution −
Example
> y<-rpois(200,5) > y
Output
[1] 6 8 7 3 5 7 6 5 2 6 4 4 3 6 6 6 6 11 7 5 4 8 6 1 3 [26] 10 4 4 9 5 2 6 4 1 5 4 4 5 1 7 8 7 3 6 6 6 2 8 7 6 [51] 7 5 5 4 6 5 3 5 3 4 4 9 3 3 3 8 3 3 2 5 4 6 6 8 4 [76] 6 12 6 1 5 5 5 0 7 4 7 7 3 2 5 5 2 5 5 4 6 4 3 4 4 [101] 4 6 5 1 2 4 4 4 8 5 8 6 3 4 5 2 3 3 3 6 7 4 4 5 3 [126] 5 5 5 8 2 5 8 1 2 3 5 9 4 3 5 6 3 6 3 6 3 7 4 4 1 [151] 3 5 0 7 2 9 6 10 2 6 4 5 1 7 2 8 7 4 2 5 4 2 4 5 6 [176] 3 9 3 9 5 9 7 3 1 3 9 5 6 3 10 7 5 5 6 7 4 2 5 5 1
Example
> chisq.test(y,p=rep(1/200,200)) Chi-squared test for given probabilities data: y X-squared = 203.61, df = 199, p-value = 0.3964 Warning message: In chisq.test(y, p = rep(1/200, 200)) : Chi-squared approximation may be incorrect
Example
> a<-sample(0:9,100,replace=TRUE) > a
Output
[1] 4 6 1 8 1 7 3 9 8 5 4 0 7 2 2 4 6 2 1 2 1 9 1 3 1 9 2 9 1 8 4 0 4 7 1 7 1 [38] 0 1 5 9 6 5 4 6 6 9 6 1 0 8 9 4 8 2 8 1 6 9 1 0 4 6 8 8 1 1 0 3 2 6 7 2 1 [75] 7 9 9 8 2 6 4 7 3 4 0 9 5 5 9 4 5 7 8 7 3 0 1 4 8 5
Example
> ks.test(a,pnorm) One-sample Kolmogorov-Smirnov test data: a D = 0.76134, p-value < 2.2e-16 alternative hypothesis: two-sided Warning message: In ks.test(a, pnorm) : ties should not be present for the Kolmogorov-Smirnov test > chisq.test(a,p=rep(1/100,100)) Chi-squared test for given probabilities data: a X-squared = 198.88, df = 99, p-value = 1.096e-08 Warning message: In chisq.test(a, p = rep(1/100, 100)) : Chi-squared approximation may be incorrect
Updated on 04-Jan-2021 06:48:00
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