Date: Tue, 1 Aug 2006 06:33:53 -0400
Reply-To: Peter Flom <flom@NDRI.ORG>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Peter Flom <flom@NDRI.ORG>
Subject: Re: Will a combination of multiple factors be significant even if
none of them individually is not?
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>On Mon, 31 Jul 2006 12:32:39 -0700, hil <meiexpress@GMAIL.COM> wrote:
>>I'm inexperience with data analysis. I hope I can make question clear:
>> I have a group of 5 factors, all of which are categorical, and binary,
>>in fact. I'm using GLM and Mixed to see if any of them or any
>>combination of them will make a significant contribution to my
>>dependent variable. Individually, none of them is significant, that
>>is, the p-values (numbers under "Pr > F") are much higher than 0.05.
>>Even none of the combinations of any 2 or 3 of these factors are
>>significant. However, one combination of 4 of them are shown to be
>>significant, with the p-value being 0.04.
>>I'm wondering if I can conclude that the combination of these 4 factors
>>is influential to the dependent variable. I asked around, and it seems
>>like statisticians would disagree, saying that if a lower-level factor
>>is not influential, at a higher-level, the combination of them will not
>>be influential. On the other hand, people with business background
>>tend to agree that even though individual factors do not make
>>difference, their combination might. So I'd like to get some opinions
There are two issues (at least).
1. As others have pointed out, you certainly can have a significant interaction with no main effects. Here's some simple made up data. Let's say you have two dichotomous variables A and B, either of which can be Yes or No, and a continuous DV, and averages like this
The main effects are 0, but there is a strong interaction
2. You may be getting into other problems with models. If you have 4 IVs, then you are testing a LOT of models. If you have strong reason to suspect a 4 way interaction, then go for it. Akso, if the intereacti makes some sort of sense, good.
But if this came about through the dreaded STEPWISE, be very careful
Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)