On 13 Feb 2001 01:38:35 -0800, [EMAIL PROTECTED] (Will Hopkins)
wrote:
> Rich Ulrich wrote:
> >You can use t-tests
> >effectively on outcomes that are dichotomous variables, and you use
> >the pooled version (Student's t) despite any difference in variances.
> >That is the test that gives you the proper p-levels.
WH >
> Rich, if the sample sizes in the two groups are different, you have to use
> the t test jigged for unequal variances. That's what my simulations showed.
>
> Your other commments about the robustness of t tests for Likert scales are
> reassuring, and thanks for responding. I did find that the confidence
> interval went awry when responses got too stacked up on the first or last
> level.
And what were the conditions of your simulations, the ones that
seemed to show a need for testing with 'unequal variances'?
- I assume that those were for Likert examples, not dichotomies.
I have been pleased with how well the Student's t performed with
dichotomies, and annoyed at how badly the Unequal-var test performed.
I can show those with EXAMPLES rather than randomizations.
I just re-did a couple, to make sure that I was not remembering them
wrong. Because I don't remember seeing these comparisons in public
before, I will show the results below:
- Here are statistics (from SPSS) for the 2x2 table, and
for the two t-tests that can be performed. I consider the primary,
useful test to be the Pearson chisquared (no correction for
continuity). The Student's t and the Pearson chisquared are
practically identical in the first table; and in the second table,
the Unequal var. t is again far off the mark by every comparison.
These tables are lined up for fixed font; but the lines
are short enough that they should usually not-wrap.
====================== summary of 2x2 statistics
10% (of 20) vs 1% (of 100)
18 | 2
99 | 1
Chi-Square Value DF Significance
-------------------- ------- ---- ------------
Pearson 5.54 1 .0186
Continuity Correction 2.46 1 .117
Likelihood Ratio 3.85 1 .0496
Mantel-Haenszel test for 5.49 1 .0191
linear association
Fisher's Exact Test:
One-Tail .07
Two-Tail .07
- - - - - - - -
t-test, pooled var 2.39 118 .018
t-test, sep.means .01 vs .1 1.29 19.8 .21
t-test, sep.means 1.84 vs 1.33 1.53 2.04 .26
================ #1
Means of 0.01 vs 0.1
Levene's Test for Equality of Variances: F= 24.0 P= .000
================ #2
Means of 1.84 vs 1.33
Levene's Test for Equality of Variances: F= 1.59 P= .210
1% (of 100) vs 10% (of 200)
99 | 1
180 | 20
Chi-Square Value DF Significance
-------------------- ------- ---- ------------
Pearson 8.29 1 .00398
Continuity Correction 6.97 1 .0083
Likelihood Ratio 10.94 1 .00094
Mantel-Haenszel test for 8.26 1 .00404
linear association
- - - - - - - -
t-test, pooled var 2.91 298 .009
t-test, sep.means .01 vs .1 3.83 270.2 .000
t-test, sep.means 1.54 vs 1.95 5.53 36.8 .000
================ #1
Means of 0.01 vs 0.1
Levene's Test for Equality of Variances: F= 40.9 P= .000
================ #2
Mean of 1.64 vs 1.95
Levene's Test for Equality of Variances: F= 127.3 P= .000
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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