Suppose you have a set of point data which contains two variables (say var1 and var2), both of which have discrete values (say 1, 2, and 3). You try to map them (see attached files var1.jpeg and var2.jpeg for reference) and decide you want to see how similar these two data are in terms of statistics. You create a "matrix" comparing the values of the two variables (see sim.jpg) and obtain a %similarity by taking the percentage of the total count of all points which had the same value for both variables (e.g. var1 and var2 = 1, etc.) in relation to the total number of points.
Is that the only way to compare the two variables? What other methods can be performed to compare these two?
P.S.: Scatter plots are ineffective, since they only result in a set of 9 visible points (because the data is discrete, the only possible values for each axis is 1, 2 and 3, resulting in only 9 possible combinations of ordered pairs) (see scatter.jpg). Q-Q plots only show 5 points (see qq.jpg).
Thank you very much!
If you want to make the statistical comparison between two functions it is possible to use the covariance functions. This is a procedure that will allow you to find statistical similarities between two time series. For this there is the theoretical definition from the integration operations and also several available computing algorithms. I recommend using the Matlab application which has built-in almost all covariance functions.
The Cramer’s V indicates relationship coefficient for discrete values.
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