Documentation

The R_K correlation coefficient can be computed from either computed KxK confusion matrices or two tables of NxK data points. The former, the discrete version, is computed using the script rkorrC and the latter by the script rkorr. In both cases it is assumed that w_K = 1/K.

Compute R_K from confusion matrices
On this webserver KxK confusion matrices on the form

C_11 C_12 ... C_1K C_21 C_22 ... C_2K ... C_K1 C_K2 ... C_KK

line by line can be computed. K can differ line by line, but it is recommended that K is the same. An output example is:

R_K	K	b	b'	COV_XY	COV_XX	COV_YY	Q_K	C_11	C_12	C_13	C_21	C_22	C_23	C_31	C_32	C_33
0.75	3	0.76	0.75	1613192	2127864	2145578	0.85	213	21	12	89	459	90	29	39	958
0.79	3	0.78	0.79	5637032	7202094	7156148	0.85	984	58	23	239	929	59	95	12	894
0.05	3	0.05	0.05	3935755	83486406	83417218	0.37	34	3443	96	3467	89	32	13	49	3977

where R_K is the correlation coefficient, K the number of categories, b and b' the coefficients in the linear fits between the two data sets, and COV(X,Y), COV(X,X), COV(Y,Y) the respective expected covariances. Q_K is the normalized trace of the confusion matrix, and C_11, ..., C_33 are the elements of the confusion matrix. This was computed for the confusion matrix data example.

This option invoke the script rkorrC. [The commandline version has an option more, convenient when the script is applied in a pipe of data.]

Warning: use of different K's will imply that the header with C_ij unrealiable. The results line by line is still valid.

Compute R_K from two NxK tables of data
Here, only one single R_K can be computed at the time. The input to the webserver should be data line by line of the form (n=1,...,N)

Y_n1, Y_n2, ... , Y_nK X_n1, X_n2, ... , X_nK

An output example

R_K	b	b'	COV(X,Y)	COV(X,X)	COV(Y,Y)
0.009105	0.102038	0.000813	8.267932	81.027805	10175.492523

where R_K is the correlation coefficient b and b' the coefficients in the linear fits between Y and X (and X and Y resp.), and COV(X,Y), COV(X,X), COV(Y,Y) the respective expected covariances. This was computed for the NxK table data example.

This option invoke the script rkorr.