chi.plot(Y1, Y2, ...)plot.Perform the same transformation for the pairwise differences associated with the first observation in y$_2$. Let pairwise differences associated with the first observation in y$_2$ that are greater than zero be transformed to ones and all other differences be zeros. Take the sum of the transformed values, and let this sum divided by (1 - n) be be the first element in the 1 x n vector g. Find the rest of the elements (2,..,n) in g using the same process.
Let pairwise differences associated with the first observation in y$_1$ and the first observation in y$_2$ that are both greater than zero be transformed to ones and all other differences be zeros. Take the sum of the transformed values, and let this sum divided by (1 - n) be be the first element in the 1 x n vector h. Find the rest of the elements (2,..,n) in h using the same process. We let: $$S = sign((\bold{z} - 0.5)(\bold{g} - 0.5))$$ $$\chi =(\bold{h} - \bold{z} \times \bold{g})/\sqrt{\bold{z} \times (1 - \bold{z}) \times \bold{g} \times (1 - \bold{g})}$$ $$\lambda = 4 \times \emph{S} \times max[(\bold{z} - 0.5)^2,(\bold{g} - 0.5)^2]$$
We plot the resulting paired $\chi$ and $\lambda$ values for values of $\lambda$ less than $4(1/(n - 1) - 0.5)^2$. Values outside of $\frac{1.78}{\sqrt{n}}$ can be considered non-independent.
Fisher, N. I, and Switzer, P. (1985) Chi-plots for assessing dependence. Biometrika, 72: 253-265.
Fisher, N. I., and Switzer, P. (2001) Graphical assessment of dependence: is a picture worth 100 tests? The American Statistician, 55: 233-239.
bv.boxplotY1<-rnorm(100, 15, 2)
Y2<-rnorm(100, 18, 3.2)
chi.plot(Y1, Y2)
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