Posted by
Mike on
May 20, 2015; 2:07pm
URL: http://spssx-discussion.165.s1.nabble.com/categorical-data-analysis-question-tp5729576p5729581.html
On Wednesday, May 20, 2015 9:27 AM, Bruce Weaver wrote:
> Good morning Gene. You say you want "to see to what extent scale
> items have
> the same frequency distribution". I think that translates to
> comparing the
> marginal frequencies (or probabilities) for a series of 4x4 tables.
> From
> the FM entry for CROSSTABS > STATISTICS:
>
> MCNEMAR. Display a test of symmetry for square tables. The McNemar
> test is
> displayed for 2 x 2 tables,
> and the McNemar-Bowker test, for larger tables.
>
> If there is some generalization of Bowker's test for tables of higher
> dimensions (e.g., 4x4x4), I am unaware of it.
I readily admit that I know little in this area and have even less
interest
in developing that knowledge but I am aware of at least two papers that
may be relevant. See:
Evans, G. T., & Hoenig, J. M. (1998). Testing and viewing symmetry
in contingency tables, with application to readers of fish ages.
Biometrics, 620-629.
Available on Jstor or try:
http://www.fisheries.vims.edu/hoenig/pdfs/Viewing.pdfNOTE: the methods here apply to cubes and hypercubes.
Contreras-Cristán, A., & González-Barrios, J. M. (2009). A Nonparametric
Test for Symmetry Based on Freeman and Halton's Ideas on Contingency
Tables. Communications in Statistics-Simulation and Computation,
38(9), 1856-1869.
The abstract for the above follows:
In this article, we propose a nonparametric method to test for symmetry
in bivariate data. By using the extension of Fisher's exact treatment
for
2 × 2 contingency tables proposed by Freeman and Halton (1951), we
can test the hypothesis of equal distribution for two samples of integer
valued variables. Then, by counting the number of observations belonging
to each cell of a symmetric, appropriately built grid, we can produce
the
two samples of integers required to use this test for equal
distribution.
The resulting test for symmetry is potentially extendible to higher
dimensions.
A simulation study is performed to compare with some known tests
(Bowker, 1948; Hollander, 1971; and its improvement given in Krampe and
Kuhnt, 2007). Our proposal represents a competitive option as a test for
symmetry.
NOTE: PDF is available on EBSCOhost and probably other sources.
Might be free on the internet but one would have to sniff it out.
Clearly this goes beyond SPSS but it is possible that there is code
that implements the ideas in the above papers (maybe in R?) or
one can roll one's own if they understand the mathematics.
HTH.
-Mike Palij
New York University
[hidden email]
> For visual comparison of the distributions, I think clustered bar
> charts
> would do the trick.
>
> HTH.
>
>
>
> Maguin, Eugene wrote
>> I have 4-point likert type responses to survey items that are
>> supposed to
>> define several scales. Some items on each scale are reversed. Perhaps
>> this
>> is a poorly considered idea but what I'd like to do, after reversing
>> the
>> reversed items, is to see to what extent scale items have the same
>> frequency distribution. I was looking through the selection of
>> non-parametric tests and it seems that the Friedman test might be
>> appropriate. However, (Q1) the Friedman is described as being for
>> 'related' samples. I am unsure of the meaning of 'related samples?
>> Help
>> please.
>>
>> Q2. Is there a better way to go at this?
>>
>> Thanks, Gene Maguin
>>
>>
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>
>
> -----
> --
> Bruce Weaver
>
[hidden email]
>
http://sites.google.com/a/lakeheadu.ca/bweaver/>
> "When all else fails, RTFM."
>
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