;$Id: //depot/Release/ENVI50_IDL82/idl/idldir/lib/tm_test.pro#1 $
;
; Copyright (c) 1994-2012, Exelis Visual Information Solutions, Inc. All
; rights reserved. Unauthorized reproduction is prohibited.
;+
; NAME:
; TM_TEST
;
; PURPOSE:
; This function computes the Student's t-statistic and the probability
; that two vectors of sampled data have significantly different means.
; The default assumption is that the data is drawn from populations with
; the same true variance. This type of test is often refered to as the
; T-means Test.
;
; CATEGORY:
; Statistics.
;
; CALLING SEQUENCE:
; Result = TM_TEST(X, Y)
;
; INPUTS:
; X: An n-element vector of type integer, float or double.
;
; Y: An m-element vector of type integer, float or double.
; If the PAIRED keyword is set, X and Y must have the same
; number of elements.
;
; KEYWORD PARAMETERS:
; PAIRED: If set to a non-zero value, X and Y are assumed to be
; paired samples and must have the same number of elements.
;
; UNEQUAL: If set to a non-zero value, X and Y are assumed to be from
; populations with unequal variances.
;
; EXAMPLE
; Define two n-element vectors of tabulated data.
; X = [257, 208, 296, 324, 240, 246, 267, 311, 324, 323, 263, 305, $
; 270, 260, 251, 275, 288, 242, 304, 267]
; Y = [201, 56, 185, 221, 165, 161, 182, 239, 278, 243, 197, 271, $
; 214, 216, 175, 192, 208, 150, 281, 196]
; Compute the Student's t-statistic and its significance assuming that
; X and Y belong to populations with the same true variance.
; The result should be the two-element vector [5.5283890, 2.5245510e-06],
; indicating that X and Y have significantly different means.
; result = tm_test(X, Y)
;
; PROCEDURE:
; TM_TEST computes the t-statistic of X and Y as the ratio;
; (difference of sample means) / (standard error of differences) and
; its significance (the probability that |t| could be at least as large
; large as the computed statistic). X and Y may be of different lengths.
; The result is a two-element vector containing the t-statistic and its
; significance. The significance is a value in the interval [0.0, 1.0];
; a small value (0.05 or 0.01) indicates that X and Y have significantly
; different means.
;
; REFERENCE:
; Numerical Recipes, The Art of Scientific Computing (Second Edition)
; Cambridge University Press
; ISBN 0-521-43108-5
;
; MODIFICATION HISTORY:
; Written by: GGS, RSI, Aug 1994
; TM_TEST is based on the routines: ttest.c, tutest.c and
; tptest.c described in section 14.2 of Numerical Recipes,
; The Art of Scientific Computing (Second Edition), and is
; used by permission.
; CT, RSI, March 2000: removed redundant betacf, ibeta functions
;-
function tm_test, x0, x1, paired = paired, unequal = unequal
on_error, 2
if keyword_set(paired) ne 0 and keyword_set(unequal) ne 0 then $
message, 'Paired and Unequal keywords cannot be set simultaneously.'
nx0 = n_elements(x0)
nx1 = n_elements(x1)
if nx0 le 1 or nx1 le 1 then $
message, 'x0 and x1 must be vectors of length greater than one.'
type = size(x0)
if keyword_set(paired) ne 0 then begin
;x0 and x1 are paired samples with corrected covariance.
if nx0 ne nx1 then message, $
'Paired keyword requires vectors of equal size.'
mv0 = moment(x0)
mv1 = moment(x1)
cov = total((x0 - mv0[0]) * (x1 - mv1[0]))
df = nx0 - 1
cov = cov / df
sd = sqrt((mv0[1] + mv1[1] - 2.0 * cov) / nx0)
t = (mv0[0] - mv1[0]) / sd
prob = ibeta(0.5*df, 0.5, df/(df+t^2))
if type[2] eq 4 then return, float([t, prob]) $
else return, [t, prob]
endif else if keyword_set(unequal) ne 0 then begin
;x0 and x1 are assumed to have different population variances.
mv0 = moment(x0)
mv1 = moment(x1)
t = (mv0[0] - mv1[0]) / sqrt(mv0[1]/nx0 + mv1[1]/nx1)
df = (mv0[1]/nx0 + mv1[1]/nx1)^2 / $
((mv0[1]/nx0)^2/(nx0 - 1.0) + (mv1[1]/nx1)^2/(nx1 - 1.0))
prob = ibeta(0.5*df, 0.5, df/(df+t^2))
if type[2] ne 5 then return, float([t, prob]) $
else return, [t, prob]
endif else begin
;x0 and x1 are assumed to have the same population variance.
mv0 = moment(x0)
mv1 = moment(x1)
df = nx0 + nx1 - 2
var = ((nx0 - 1)*mv0[1] + (nx1 - 1)*mv1[1]) / df
t = (mv0[0] - mv1[0]) / sqrt(var*(1.0/nx0 + 1.0/nx1))
prob = ibeta(0.5*df, 0.5, df/(df+t^2))
if type[2] ne 5 then return, float([t, prob]) $
else return, [t, prob]
endelse
end