# HG changeset patch
# Parent 91a4bdf7a16a66e4c46ea76e9cc7aa08f53bf755
corr.m: obtain p-values from r-to-t transformation; return NaN for 1 observation.
* when correlating data sets with one observation, return NaN instead of 1.
* use a transformation into a t-distributed variable (assuming the input
variables are uncorrelated bivariate Gaussian) to obtain both-sided p-values
diff --git a/scripts/statistics/base/corr.m b/scripts/statistics/base/corr.m
--- a/scripts/statistics/base/corr.m
+++ b/scripts/statistics/base/corr.m
@@ -46,7 +46,7 @@
## Created: March 1993
## Adapted-By: jwe
-function retval = corr (x, y = [])
+function [retval, pval] = corr (x, y = [])
if (nargin < 1 || nargin > 2)
print_usage ();
@@ -54,12 +54,14 @@
## Input validation is done by cov.m. Don't repeat tests here
- ## Special case, scalar is always 100% correlated with itself
+ ## Special case, correlation for a scalar is not defined
if (isscalar (x))
if (isa (x, "single"))
- retval = single (1);
+ retval = single (NaN);
+ pval = single (NaN);
else
- retval = 1;
+ retval = NaN;
+ pval = NaN;
endif
return;
endif
@@ -76,6 +78,39 @@
retval = c ./ (s * s');
endif
+ if (nargout >= 2)
+ ## CAUTION: Currently, we always interpret a vector X or Y as having
+ ## as many observations as elements, regardless of orientation.
+ if (isvector (x))
+ numobs = numel (x);
+ else
+ numobs = size (x, 1);
+ end
+
+ if (numobs <= 2)
+ pval = NaN (size (retval));
+ else
+ pval = pval_t (retval, numobs);
+ end
+ end
+
+endfunction
+
+
+# Obtain p-values from correlation coefficients using the transformation into a
+# t-distributed variable (assuming the input variables are uncorrelated
+# bivariate Gaussian.)
+#
+# http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#Inference
+# "Testing using Student's t-distribution"
+function pval = pval_t (r, n)
+ ## Clamp to [-1+eps/2, 1-eps/2] to make the expression below always
+ ## well-defined.
+ r(r <= -1) = -1 + 0.5*eps;
+ r(r >= 1) = 1 - 0.5*eps;
+
+ x = -abs (r) .* sqrt ((n - 2) ./ (1 - r .^ 2));
+ pval = 2 * tcdf (x, n - 2);
endfunction