Chi-square distribution and degrees of freedom

Chi-square test is the goodness of fit between a set (or vector) of observed values and expected values. Chi-square is one among other distributions.

Typical chi-square distribution can be plotted with following R code:

x = seq(0, 30, length.out = 200)
plot(x,dchisq(x=x, df=2), col=33, type = 'l', xlab = 'Degrees of Freedom', ylab='Density for the chi^2 distribution')
for (i in 3:15){
  ix = dchisq(x=x, df=i)

Resulting in this


With higher Degrees of Freedom, the density of chi-square distribution is getting smaller.

We could also plot distribution function, quantile function and random generation, besides density function, switching dchisq command to pchisq or qchisq or rchisq.


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