categorical data analysis question

[Maguin, Eugene]

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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[David Marso]

Related samples:  The same persons responded to both questions.

[Bruce Weaver]

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.  

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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[Mike]

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.pdf
NOTE: 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
>>
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>
>> LISTSERV@.UGA
>
>>  (not to SPSSX-L), with no body text except the
>> command. To leave the list, send the command
>> SIGNOFF SPSSX-L
>> For a list of commands to manage subscriptions, send the command
>> INFO REFCARD
>
>
>
>
>
> -----
> --
> Bruce Weaver
> [hidden email]
> http://sites.google.com/a/lakeheadu.ca/bweaver/
>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
>
> --
> View this message in context:
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> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
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[Art Kendall]

You could also try 2D and 3D scatterplots.  (by using colors and or shapes) you could put 4 or 5 variables in the graphic.  In the output file you could use the editor to rotate graphic and view it from different perspectives.

Given that these are Likert items, the zero order correlation, corrected item-total correlations,  squared multiple correlations, and alpha if item deleted  are more conventional in reviewing item quality.


WRT 4 point response scale. If you are involved in writing the items that represent a construct via a scale, I lean toward having as many points on the response scale as is practical given the respondents' capabilities.  This helps the resulting scale be more fine-grained.  When the underlying construct is continuous, it is intuitive to have the coarse repeated measures of a construct be as close to continuous as is practical under the circumstances.

In some disciplines it appears that 4 point response scales made the use a counter-sorter easier, i.e., the deck of punch cards had to be passed through more frequently. Counter-sorters are now found in historical exhibits.  

[Rich Ulrich]

"Perhaps this is a poorly considered idea ..." -- what is bad, the scale or your idea?
Are you trying to investigate whether having reversed-items results in different scaling?

 - Please consider, "different scaling" is the REASON for having reversed items, to
discount what is called "response bias".  If response bias is what you are interested
in establishing, see my last paragraph, below.

For those who are not familiar with the theoretical approach:
The early scale developers in the 1930s noted that there will be *some* (not all)
responders who will tend to favor the positive (or negative) responses.  When that
happens and all the items are asked in the same direction, then the user's score
will be a sum of his inherent tendency on the scale, plus (or minus)  "response bias."
That is undesirable.  How do we get rid of response bias?

The simple solution is to construct scales that have equal numbers of items that
are answered in each direction, so that the "bias" averages out.  Thus, you have
manuals and guidebooks that tell investigators that it is ideal to have items this way.
In practice, this observation led to a problem that I noted, even before I studied
up on scales, where scale writers wrote terrible items -- by syntax, ease of reading,
whatever criterion -- in order to change the direction of half the answers.  (I hope
this rarely happens any more, and that the word got around that the "cure" for
response bias can be worse than the disease.)

In any case:  I noticed long ago that when I had a (decent) scale with many items
reversed, I could detect the response bias by performing a factor analysis:  The solution
of a factor analysis of items-as-initially-scored would typically produce one factor with
all loadings positive, possibly in the unrotated solution rather than the varimax solution.
Given the opposite scalings, that factor measures response bias.  This would not be the
largest factor, but I think I saw it when the N was large enough to show structure for
other known factors.

--
Rich Ulrich

---

Date: Tue, 19 May 2015 21:59:53 +0000
From: [hidden email]
Subject: categorical data analysis question
To: [hidden email]

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?

 

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD