[SciPy-user] Welch's ttest

[Angus McMorland]

On 15/08/07, Alan G Isaac <aisaac at american.edu> wrote:
> On Tue, 14 Aug 2007, Angus McMorland apparently wrote:
> > def welchs_approximate_ttest

> Just a reminder that nowadays if you post code it is
> helpful to state explicitly what the license is,
> even if you think it is simple enough to obviously
> belong in the public domain.  On this list,
> public domain, BSD, or MIT licensing are particularly
> welcome, I believe.

An excellent reminder, thanks Alan. After a quick check to remind
myself what these all mean, the BSD licence will do fine for that
code. For completeness then, the code becomes:

def welchs_approximate_ttest(n1, mean1, sem1, \
                            n2, mean2, sem2, alpha):
    '''Welch''s approximate t-test for the difference of two means of
heteroscedasctic populations.

Implemented from Biometry, Sokal and Rohlf, 3rd ed., 1995, Box 13.4

:Parameters:
    n1 : int
        number of variates in sample 1
    n2 : int
        number of variates in sample 2
    mean1 : float
        mean of sample 1
    mean2 : float
        mean of sample 2
    sem1 : float
        standard error of mean1
    sem2 : float
        standard error of mean2
    alpha : float
        desired level of significance of test

:Returns:
    significant : bool
        True if means are significantly different, else False
    t_s_prime : float
        t_prime value for difference of means
    t_alpha_prime : float
        critical value of t_prime at given level of significance

Copyright (c) 2007, Angus McMorland

All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright
    notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
    * Neither the name of the University of Auckland, New Zealand nor
    the names of its contributors may be used to endorse or promote
    products derived from this software without specific prior written
    permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL,EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.'''
    svm1 = sem1**2 * n1
    svm2 = sem2**2 * n2
    t_s_prime = (mean1 - mean2)/n.sqrt(svm1/n1+svm2/n2)
    t_alpha_df1 = scipy.stats.t.ppf(1-alpha/2, n1 - 1)
    t_alpha_df2 = scipy.stats.t.ppf(1-alpha/2, n2 - 1)
    t_alpha_prime = (t_alpha_df1 * sem1**2 + t_alpha_df2 * sem2**2) / \
                    (sem1**2 + sem2**2)
    return abs(t_s_prime) > t_alpha_prime, t_s_prime, t_alpha_prime

and a test class as well...

class TestBiometry(NumpyTestCase):
    def test_welchs_approximate_ttest(self):
        chimpanzees = (37, 0.115, 0.017) # n, mean, sem
        gorillas = (6, 0.511, 0.144)
        case1 = welchs_approximate_ttest(chimpanzees[0], \
                                    chimpanzees[1], \
                                    chimpanzees[2], \
                                    gorillas[0], \
                                    gorillas[1], \
                                    gorillas[2], \
                                    0.05)
        self.assertTrue( case1[0] )
        self.assertAlmostEqual( case1[1], -2.73, 2 )
        self.assertAlmostEqual( case1[2], 2.564, 2 )

        female = (10, 8.5, n.sqrt(3.6)/n.sqrt(10))
        male = (10, 4.8, n.sqrt(0.9)/n.sqrt(10))
        case2 = welchs_approximate_ttest(female[0], \
                                female[1], \
                                female[2], \
                                male[0], \
                                male[1], \
                                male[2], 0.001)
        self.assertTrue( case2[0] )
        self.assertAlmostEqual( case2[1], 5.52, 2 )
        self.assertAlmostEqual( case2[2], 4.781, 2 )

In case it's useful to anyone the standard form of the BSD licence can
be found here: http://www.opensource.org/licenses/bsd-license.php

> IMO, there should be an explicit policy that code
> posted to the list without a licensing statement
> will be in the public domain.  I believe that is
> the intent of such posts, in general. But this policy
> should be presented as part of the list registration.

Sounds like a good plan to me.

> Cheers,
> Alan Isaac
-- 
AJC McMorland, PhD Student
Physiology, University of Auckland