![]() This correlation is also not significantly different from 0. Similarly, if you sort the Weight variable in decreasing order (WeightDecr), the sorted values have -0.09 correlation with the Height variable. This correlation is not significantly different from 0. However, if you sort the weight variable in increasing order (WeightIncr), the sorted values have 0.06 correlation with the height values. The output shows that the original variables were highly correlated. * what is the correlation between the first variable and permutations of the second variable? */ proc corr data=Class2 nosimple * add the sorted variables to the original data */ data Class2 Proc sort data=Class ( keep=Weight ) out=Weight2 ( rename= (Weight=WeightDecr ) ) * sort only the second variable: First increasing order, then decreasing order */ proc sort data=Class ( keep=Weight ) out=Weight1 ( rename= (Weight=WeightIncr ) ) The Height and Weight variables are highly correlated (R = 0.88), as shown by the following call to PROC CORR in Base SAS: The Sashelp.Class data set in SAS contains observations about the height, weight, age, and gender of 19 students. You can use this technique to construct a new vector that has the same values (marginal distribution) but almost any correlation you want with the other vector.Ī simple permutation: A sorted vector of values This article looks at how sorting one variable (independently of another) changes the correlation between two variables. The goal of a permutation test is to determine whether the original statistic is likely to be observed in a random pairing of the data values. In a permutation test, you repeatedly change the order of one of the variables independently of the other variable(s). This observation is the basis behind permutation tests for paired data values. If you sort Y independently and call the vector of sorted observations Z, then corr(X,Z) is typically not equal to corr(X,Y), even though Y and Z contain exactly the same data values. This statement is both obvious and profound.įor example, the correlation between two variables X and Y depends on the (X,Y) pairs. You cannot sort an individual variable (independently) if you want to preserve its relationship with other variables. If you sort univariate data, the mean and standard deviation do not change. For many univariate statistics (mean, median, standard deviation, etc.), the order of the data is unimportant. ![]()
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