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Date:         Wed, 3 Nov 2004 13:59:15 -0800
Reply-To:     huixin fei <hxfei@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         huixin fei <hxfei@YAHOO.COM>
Subject:      Re: chi square follow-up tests and type I correction
Comments: To: Serge Sévigny <serge.sevigny@PSY.ULAVAL.CA>
In-Reply-To:  <Lcaid.153535$0f.85405@charlie.risq.qc.ca>
Content-Type: text/plain; charset=us-ascii

Dale suggested using the GLIMMIX procedure (SAS V9.1) a couple of month ago. I re-attached this message in this list.

John Fei > > > Dale McLerran <stringplayer_2@YAHOO.COM> wrote:Stephen, > > I don't believe that SAS has such a procedure. However, it could > easily be implemented using data step code. Whether you should > or not is another question. I am not sure that the Marascuillo > multiple proportion comparison procedure is all that great. In > the example given at the website that you referred to, the global > test for differences among the proportions is significant at the > alpha=0.05 level. However, none of the pairwise contrasts are > significantly different. This seems quite peculiar, especially > since the number of samples for each of the five lots being > compared are equal. The global test has enough information to > find significant differences in the sample defect rate, but there > is not enough information to identify even one contrast where > there is a difference? > > Now, how about an easily implemented alternative. An alternative > to the chi-square test for equality of proportions would be to > fit a logistic regression model with defects as the response and > lot as the predictor variable. Now, the procedures LOGISTIC, > CATMOD, and GENMOD can all fit a logistic regression, but none > have an LSMEANS statement which allows multiple comparisons. > (GENMOD has an LSMEANS statement, but it does not support > multiple comparisons testing. The other two do not have any > LSMEANS statement.) However, you can use the GLIMMIX macro - or > the new GLIMMIX procedure! - to fit a logistic regression model. > Both the GLIMMIX macro and procedure have LSMEANS statements which > allow multiple comparison tests to be performed. > > Let me demonstrate with the data presented on the website that > you referred to. > > /* Construct data of defect rates in 5 lots */ > data test; > samples=300; > lot=1; defects=36; link binary; > lot=2; defects=46; link binary; > lot=3; defects=42; link binary; > lot=4; defects=63; link binary; > lot=5; defects=38; link binary; > binary: > /* Output a record for each of the 1800 observations */ > do i=1 to defects; > defect=1; > output; > end; > do i=1 to samples-defects; > defect=0; > output; > end; > return; > run; > > > /* Construct the usual chi-square test that the */ > /* proportion of defects are the same across all lots */ > proc freq data=test; > tables defect*lot / chisq; > run; > > > /* Use the GLIMMIX macro to */ > /* 1) construct a global test that can be compared */ > /* with the chi-square test formed above */ > /* 2) form and test pairwise comparisons, allowing */ > /* for multiple comparison adjustments */ > %glimmix(data=test, > stmts=%str(class lot; > model defect = lot; > lsmeans lot / diff adjust=tukey; > )) > > > You will observe that the overall F-test for the effect of LOT > has very nearly the same p-value as the chi-square test. > Asymptotically, the two tests would be equivalent. We may > actually prefer the overall F-test obtained from the logistic > regression - especially if the sample sizes were small. Here, > sample size is large enough that the two approaches yield very > similar global test statistics. > > Having satisfied that the global test is providing an equivalent > overall test, we can look at the pairwise comparisons obtained > out of the LSMEANS statement. I employed a Tukey multiple > comparison adjustment. You will observe that three comparisons > are identified as significant > > 1) the contrast between lots 1 and 4 > 2) the contrast between lots 3 and 4 > 3) the contrast between lots 5 and 4 > > In addition, the contrast between lots 2 and 4 is significant > at alpha<0.075. None of the other contrasts even approach > significance. Thus, our test identifies significant pairwise > contrasts that the Marascuillo test does not. > > It is easy to generalize this to a model where you have multiple > factors (lots within week and lots between weeks). I think that > it would be best to construct your data with day of the week > and week. Then you could test whether there were more failures > on, say, Monday or on Friday. A priori hypotheses about day > of the week may be dealt with employing GLIMMIX. You probably > do not want to employ multiple comparison tests where an a priori > hypothesis could be constructed. You would likely not have any > a priori hypothesis that a certain weeks would have more failures > than other weeks. Thus, you could use multiple comparison > adjustments to test pairwise differences between weeks. You > could test specific day of week contrasts without resorting to > the penalty that a multiple comparisons procedure produces. > > Note that the GLIMMIX procedure is available only for SAS version > 9.1 with Windows OS. The GLIMMIX macro has been distributed > with SAS for quite a few years, so should be readily available. > > > Dale > > --- Stephen Arthur wrote: > > > Hello, > > > > Is the Marascuillo multiple proportion comparison procedure > included > > in > > SAS? > > > > http://www.itl.nist.gov/div898/handbook/prc/section4/prc474.htm > > > > I did a search on the SAS website and the searches: > > 1) Marascuillo > > 2) +"multiple comparison" and proportion > > > > turned up zero results. > > http://sas.com/search/index.html > > > > Also, does anyone know of a two-way Marascuillo multiple proportion > > comparison procedure... maybe this doesn't make sense, I'll have to > > think > > about it some more. > > > > Basically, I have an analysis situation where I want to test the > > significance of proportions within a week, and between weeks. The > > data is > > very randomly collected (unbalance sample sizes and missing data), > > these > > are not controlled studies. > > > > Thanks, > > > > Stephen > > > > > ===== > --------------------------------------- > Dale McLerran > Fred Hutchinson Cancer Research Center > mailto: dmclerra@fhcrc.org > Ph: (206) 667-2926 > Fax: (206) 667-5977 > --------------------------------------- > > Huixin,

I really don't know the MULTTEST procedure at all. You might be able to perform appropriate post hoc multiple comparisons for proportions employing the MULTTEST procedure. I simply do not know. Sorry.

Dale

--- huixin fei <hxfei@yahoo.com> wrote:

> > Thank you very much for this information. I have to test the > proportions among the > > treatments (and do “post hoc?multiple comparisons) in a biological > environment, a > > similar problem. I tried to use multiple Z tests with Bonferroni’s > adjustment. > > Now I can try the GLIMMIX procedure. Could I use the Proc multtest? > > I just started to learn this procedure. Thanks. > > > > Sincerely, > > > Huixin Fei

Serge Sévigny <serge.sevigny@PSY.ULAVAL.CA> wrote:Hi, suppose we have a significant chi square on a 3 (a, b, c) by 4 ( 1, 2, 3, 4) crosstab. Now we know that the proportions differ somewhere. But we want to know exactly where :

A) Are the proportions between a and b equal? Are the proportions between a and c equal? Are the proportions between b and c equal?

1- what would be the most powerful test(s) to investigate this follow-up?

B) Then, suppose we find that the proportions between a and b are different, how do we check if they are different at 1, or 2, or 3, or 4?

2- what would be the most powerful test(s) to investigate this follow-up?

3- For all follow-up tests, do I use a bonferonni correction?

4- Do you know of a good reference book on that matter?

Thanks for helping! Serge

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