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followup tests on chi-square

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followup tests on chi-square

Jordan Kennedy
Hi all:
 
I have a 2 X 4 contingency Table that I ran a chi-square test of independence on using the Crosstabs procedure. This overall test was statistically significant. I would now like to isolate where the statistically significant differences are. How should proceed to conduct these followup tests both conceptually and then in SPSS? Thanks in advance.
 
Jordan
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Re: followup tests on chi-square

Keith McCormick
Hi Jordan,

There is no direct way to do exactly as you describe in the Crosstabs procedure. However you have at least one option, and maybe two.

1) I like to request standardized residuals (under 'cells') and look for cells that have a value outside of +/- 1, and especially outside +/- 3. This will not give you an additional hypothesis test, but it can be very revealing. When presenting a significant crosstab I usually focus my audience's attention on the largest (absolute value) standardized residuals.

2) If you have Custom Tables you can request Z-tests (under 'test statistics') on the columns. This is only possibly on the columns so you may need to think about which is your row and which is you column variable.

HTH, Keith
www.keithmccormick.com

On Thu, May 13, 2010 at 5:45 PM, Jordan Kennedy <[hidden email]> wrote:
Hi all:
 
I have a 2 X 4 contingency Table that I ran a chi-square test of independence on using the Crosstabs procedure. This overall test was statistically significant. I would now like to isolate where the statistically significant differences are. How should proceed to conduct these followup tests both conceptually and then in SPSS? Thanks in advance.
 
Jordan

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Re: followup tests on chi-square

Bruce Weaver
Administrator
In reply to this post by Jordan Kennedy
Jordan Kennedy wrote
Hi all:

I have a 2 X 4 contingency Table that I ran a chi-square test of
independence on using the Crosstabs procedure. This overall test was
statistically significant. I would now like to isolate where the
statistically significant differences are. How should proceed to conduct
these followup tests both conceptually and then in SPSS? Thanks in advance.

Jordan
In addition to what Keith suggested, one approach is to partition the overall table into orthogonal components.  I don't think this is discussed much in textbooks any more, but I have some notes on it here:

   http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf

See sections 2.5 to 2.7.  As you'll see there, this approach works particularly well with the likelihood ratio chi-square (sometimes called L-squared, or G-squared), because the chi-square statistics for the orthogonal components add up exactly to the chi-square statistic for the overall table, as one would expect.  I think I commented somewhere about the "warm fuzzy feeling" this creates.  ;-)

I should add that there is no point & click method for doing this in SPSS, AFAIK.   But it shouldn't be that hard to "roll your own" code to do it.

--
Bruce Weaver
bweaver@lakeheadu.ca
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.
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Re: followup tests on chi-square

Burleson,Joseph A.
to follow up on Bruce's suggestion to analyze orthogonal components, it is easiest to run a logistic regression with the 2-level variable as the dependent variable, and the 4-level variable as the predictor. by coding the predictor as a categorical variable, one can choose from the various a priori contrasts (note: not all of them are orthogonal), in decomposing what is a 3 df test of the predictor; 3 a priori orthogonal contrasts should give you what you want. be sure and note what is the "reference" group for some of the contrasts.

Joe Burleson

________________________________________
From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Bruce Weaver [[hidden email]]
Sent: 14 May 2010 10:10
To: [hidden email]
Subject: Re: followup tests on chi-square

Jordan Kennedy wrote:

>
> Hi all:
>
> I have a 2 X 4 contingency Table that I ran a chi-square test of
> independence on using the Crosstabs procedure. This overall test was
> statistically significant. I would now like to isolate where the
> statistically significant differences are. How should proceed to conduct
> these followup tests both conceptually and then in SPSS? Thanks in
> advance.
>
> Jordan
>
>

In addition to what Keith suggested, one approach is to partition the
overall table into orthogonal components.  I don't think this is discussed
much in textbooks any more, but I have some notes on it here:

   http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf

See sections 2.5 to 2.7.  As you'll see there, this approach works
particularly well with the likelihood ratio chi-square (sometimes called
L-squared, or G-squared), because the chi-square statistics for the
orthogonal components add up exactly to the chi-square statistic for the
overall table, as one would expect.  I think I commented somewhere about the
"warm fuzzy feeling" this creates.  ;-)

I should add that there is no point & click method for doing this in SPSS,
AFAIK.   But it shouldn't be that hard to "roll your own" code to do it.



-----
--
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.
--
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Re: followup tests on chi-square

Bruce Weaver
Administrator
Good idea, Joe.  I'll have to investigate that sometime (when I have some time).


Burleson,Joseph A. wrote
to follow up on Bruce's suggestion to analyze orthogonal components, it is easiest to run a logistic regression with the 2-level variable as the dependent variable, and the 4-level variable as the predictor. by coding the predictor as a categorical variable, one can choose from the various a priori contrasts (note: not all of them are orthogonal), in decomposing what is a 3 df test of the predictor; 3 a priori orthogonal contrasts should give you what you want. be sure and note what is the "reference" group for some of the contrasts.

Joe Burleson

________________________________________
From: SPSSX(r) Discussion [SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of Bruce Weaver [bruce.weaver@hotmail.com]
Sent: 14 May 2010 10:10
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Re: followup tests on chi-square

Jordan Kennedy wrote:
>
> Hi all:
>
> I have a 2 X 4 contingency Table that I ran a chi-square test of
> independence on using the Crosstabs procedure. This overall test was
> statistically significant. I would now like to isolate where the
> statistically significant differences are. How should proceed to conduct
> these followup tests both conceptually and then in SPSS? Thanks in
> advance.
>
> Jordan
>
>

In addition to what Keith suggested, one approach is to partition the
overall table into orthogonal components.  I don't think this is discussed
much in textbooks any more, but I have some notes on it here:

   http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf

See sections 2.5 to 2.7.  As you'll see there, this approach works
particularly well with the likelihood ratio chi-square (sometimes called
L-squared, or G-squared), because the chi-square statistics for the
orthogonal components add up exactly to the chi-square statistic for the
overall table, as one would expect.  I think I commented somewhere about the
"warm fuzzy feeling" this creates.  ;-)

I should add that there is no point & click method for doing this in SPSS,
AFAIK.   But it shouldn't be that hard to "roll your own" code to do it.



-----
--
Bruce Weaver
bweaver@lakeheadu.ca
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: http://old.nabble.com/followup-tests-on-chi-square-tp28559334p28559883.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
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command. To leave the list, send the command
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=====================
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--
Bruce Weaver
bweaver@lakeheadu.ca
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.
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