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.