unequal variances
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dear list my design is very simple 2X3 ANOVA (when the first variable is within subjects and the second between subjects). the effects are significant but the problem is that the variances are not equal (Levine test shows strong differences between the groups). Can somebody offer a solution (for
example a specific kind of transformation that can make the variances equal) ? I will appreciate any help Kelly Saporta, Ph.D.
Department of Education and Psychology Email:
[hidden email] http://www.openu.ac.il/Personal_sites/kelli-saporta/ |
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Kelly, you might consider running your model via MIXED. (This will require a long file format with one row per observation rather than one row per subject.) Ryan B posted an example in another thread that might help get you started:
MIXED y BY group /FIXED=group | SSTYPE(3) /PRINT=SOLUTION /REPEATED=group | SUBJECT(subject) COVTYPE(DIAG). Source: http://spssx-discussion.1045642.n5.nabble.com/Brown-Forsythe-error-in-1-way-ANOVA-tp5720253p5720273.html That example was for a one-way (between-Ss) ANOVA, but I expect you can use the same approach for your 2x3 mixed design. HTH.
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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In reply to this post by Keli Saporta
Google ‘Box-Cox transformations’. You can work through different types of transformations to equalize variances. But, here’s the real question: Why are the variances different? It could be sampling error; but what if it’s substantively meaningful? I see that you have a repeated measures design. Maybe there is an intervention involved. Why should the intervention group at post and followup have the same variances as the control group at those points? I see that Bruce has posted a specific analysis to use. You might also consider a growth curve model, which there is an example of in the documentation. Gene Maguin From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Keli Saporta dear list my design is very simple 2X3 ANOVA (when the first variable is within subjects and the second between subjects). the effects are significant but the problem is that the variances are not equal (Levine test shows strong differences between the groups). Can somebody offer a solution (for example a specific kind of transformation that can make the variances equal) ? I will appreciate any help Kelly Saporta, Ph.D. Department of Education and Psychology Email: [hidden email] http://www.openu.ac.il/Personal_sites/kelli-saporta/ |
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In reply to this post by Keli Saporta
How is the distribution of the DV? Is it symmetric and unimodal? Dr. Paul R. Swank, Professor Health Promotion and Behavioral Sciences School of Public Health University of Texas Health Science Center Houston From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Keli Saporta dear list my design is very simple 2X3 ANOVA (when the first variable is within subjects and the second between subjects). the effects are significant but the problem is that the variances are not equal (Levine test shows strong differences between the groups). Can somebody offer a solution (for example a specific kind of transformation that can make the variances equal) ? I will appreciate any help Kelly Saporta, Ph.D. Department of Education and Psychology Email: [hidden email] http://www.openu.ac.il/Personal_sites/kelli-saporta/ |
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In reply to this post by Keli Saporta
"Where do the numbers come from?" - has always been my own
starting point for figuring out transformations. Is the measurement rationally chosen in the first place? Should you have been using (say) logs of those biological measures, or square-roots of those counts? Reciprocals of distances? Two levels of "within" is often Pre-Post. "Pre-Post" sometimes has an *expectation* of big changes from a starting level, for one group or all groups. Or, for starting scores that are diverse, the changes could cause scoring to hit the scale maximum. Are you dealing with anything like these basement/ceiling effects? There are books written on analyzing "change scores", where one possibility is to ignore the starting scores. On the other hand, if you have several groups with big differences in variance between-subjects, rather than within-subjects, you have a problem that is potentially fatal for a Pre-Post study: If the groups are not comparable at Pre, how can you hope to compare changes? (Answer ... "with graphs, and a whole lot of peripheral discussion.") If the dimension Within is not time, then you don't face the issues of "changes." You need to consider whether the heterogeneity is blamed on the measurement scale, or if it is a property of the populations being sampled. "Scaling" might be readily fixed by transformations, whereas gross variability of variation requires a narrative and justification for comparing means. -- Rich Ulrich Date: Tue, 4 Jun 2013 10:24:01 +0000 From: [hidden email] Subject: unequal variances To: [hidden email] dear list
my design is very simple 2X3 ANOVA (when the first variable is within subjects and the second between subjects). the effects are significant but the problem is that the variances are not equal (Levine test shows strong differences between the groups). Can somebody offer a solution (for example a specific kind of transformation that can make the variances equal) ? I will appreciate any help
Kelly Saporta, Ph.D. Department of Education and Psychology Email: [hidden email] http://www.openu.ac.il/Personal_sites/kelli-saporta/
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In reply to this post by Bruce Weaver
Best Diana On 04/06/2013 16:06, "Bruce Weaver" <bruce.weaver@...> wrote: Kelly, you might consider running your model via MIXED. (This will require a Emeritus Professor Diana Kornbrot email: d.e.kornbrot@... web: http://dianakornbrot.wordpress.com/ Work Department of Psychology School of Life and Medical Sciences University of Hertfordshire College Lane, Hatfield, Hertfordshire AL10 9AB, UK voice: +44 (0) 170 728 4626 Home 19 Elmhurst Avenue London N2 0LT, UK voice: +44 (0) 208 444 2081 mobile: +44 (0) 740 318 1612 |
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In reply to this post by Bruce Weaver
Thank you Brauce for your answer but I am not sure that would help. The within factor variable is the story (each participant read two stories) and the between subject variable is a version of the story (emotional, neutral or rational). the problem is not with the within subjects variable but with the between subjects variable. But I will try what you suggest
-----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Bruce Weaver Sent: Tuesday, June 04, 2013 6:06 PM To: [hidden email] Subject: Re: unequal variances Kelly, you might consider running your model via MIXED. (This will require a long file format with one row per observation rather than one row per subject.) Ryan B posted an example in another thread that might help get you started: MIXED y BY group /FIXED=group | SSTYPE(3) /PRINT=SOLUTION /REPEATED=group | SUBJECT(subject) COVTYPE(DIAG). Source: http://spssx-discussion.1045642.n5.nabble.com/Brown-Forsythe-error-in-1-way-ANOVA-tp5720253p5720273.html That example was for a one-way (between-Ss) ANOVA, but I expect you can use the same approach for your 2x3 mixed design. HTH. Keli Saporta wrote > dear list > > my design is very simple 2X3 ANOVA (when the first variable is within > subjects and the second between subjects). > the effects are significant but the problem is that the variances are not > equal (Levine test shows strong differences between the groups). Can > somebody offer a solution (for example a specific kind of transformation > that can make the variances equal) ? > I will appreciate any help > > Kelly Saporta, Ph.D. > Department of Education and Psychology > The Open University, Ra'anana, Israel 43107 > Phone: +972-9-7781456, > Email: > kelisa@.ac > <mailto: > shaidanz@.ac > > > http://www.openu.ac.il/Personal_sites/kelli-saporta/ ----- -- 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: http://spssx-discussion.1045642.n5.nabble.com/unequal-variances-tp5720547p5720550.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== 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 ===================== 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 |
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You say "the problem [i.e., heterogeneity of variance] is not with the within subjects variable but with the between subjects variable." What are the sample sizes and variances for the 3 groups? ANOVA is very robust to heterogeneity of variance when the group sizes are all equal. The more discrepant the group sizes become, the more of an issue it becomes.
The rest of this assumes that you do need to be concerned about heterogenity of variance, and follows up on the suggestion I made earlier. Note that Ryan's example was for a one-way (between-Ss) ANOVA, and that I was suggesting his example as a starting point, not that you should run his syntax as is. I'm also not entirely sure that approach will work, but it might be worth investigating. Having offered all those hedges, I just found this example of a design similar to yours: * Example from http://www.appliedmissingdata.com/two-factor-mixed-anova-one.html . mixed dv by bsfactor wsfactor /method = ml /print = testcov /emmeans = tables (bsfactor*wsfactor) compare(bsfactor) /fixed = bsfactor wsfactor bsfactor*wsfactor /repeated = wsfactor | subject(id) covtype(cs). Comparing that to Ryan's example for one-way ANOVA, I would try something like this: mixed dv by bsfactor wsfactor /method = ml /print = testcov /emmeans = tables (bsfactor*wsfactor) compare(bsfactor) /fixed = bsfactor wsfactor bsfactor*wsfactor /repeated = bsfactor | subject(id) covtype(diag). But as I said, I don't know if it will work or not. HTH. p.s. - The two-factor between-within example shown above appears to have been created before the VC covariance structure became obsolete. The following is from the v20 CSR Manual: The VC covariance structure is obsolete in the REPEATED subcommand. If it is specified, it will be replaced with the DIAG covariance structure. An annotation will be made in the output to indicate this change.
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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In reply to this post by Maguin, Eugene
Hi gene This is not a pre- post design. the repeat variable is just two stories that each participant is exposed to. I think that the reason for the unequal variances is that in one of the condition (the between group variable has three level) the manipulation itself
produce a large variance. From:
SPSSX(r) Discussion [mailto:[hidden email]]
On Behalf Of
Maguin, Eugene Google ‘Box-Cox transformations’. You can work through different types of transformations to equalize variances. But, here’s the real question: Why are
the variances different? It could be sampling error; but what if it’s substantively meaningful? I see that you have a repeated measures design. Maybe there is an intervention involved. Why should the intervention group at post and followup have the same variances
as the control group at those points? I see that Bruce has posted a specific analysis to use. You might also consider a growth curve model, which there is an example of in the documentation. Gene Maguin From: SPSSX(r) Discussion [mailto:[hidden email]]
On Behalf Of Keli Saporta dear list my design is very simple 2X3 ANOVA (when the first variable is within subjects and the second between subjects). the effects are significant but the problem is that the variances are not equal (Levine test shows strong differences between the groups). Can somebody offer a solution (for
example a specific kind of transformation that can make the variances equal) ? I will appreciate any help Kelly Saporta, Ph.D.
Department of Education and Psychology Email:
[hidden email] http://www.openu.ac.il/Personal_sites/kelli-saporta/ |
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I will repeat what I said the first time. The important question for considering
any transformation (or alternate analysis) is, "Where do the numbers come from?" If someone expected the "manipulation [to] produce a large variance," they might be guilty of poor design of the outcome -- especially if the variability is not *due* to a change in the mean, and the mean is what you are committed to reporting on. However, if the one group uses (for example) all seven points of a scale, where the others mostly use the points at one extreme, it might be safe to pool the variances in the usual way, i.e., no corrections. (Even then, you might find that reviewers are happier if you use a test that does not assume equal variances.) If the one group was *expected* to be different from the other two, then the designed analysis that provides more power would be to analyze the data as just two groups, Experimental versus two Controls... which are pooled, after verifying that they do not differ. -- Rich Ulrich Date: Wed, 5 Jun 2013 03:29:37 +0000 From: [hidden email] Subject: Re: unequal variances To: [hidden email] Hi gene This is not a pre- post design. the repeat variable is just two stories that each participant is exposed to. I think that the reason for the unequal variances is that in one of the condition (the between group variable has three level) the manipulation itself produce a large variance.
From:
SPSSX(r) Discussion [mailto:[hidden email]]
On Behalf Of
Maguin, Eugene
Google ‘Box-Cox transformations’. You can work through different types of transformations to equalize variances. But, here’s the real question: Why are the variances different? It could be sampling error; but what if it’s substantively meaningful? I see that you have a repeated measures design. Maybe there is an intervention involved. Why should the intervention group at post and followup have the same variances as the control group at those points?
I see that Bruce has posted a specific analysis to use. You might also consider a growth curve model, which there is an example of in the documentation. Gene Maguin
From: SPSSX(r) Discussion [mailto:[hidden email]]
On Behalf Of Keli Saporta
dear list
my design is very simple 2X3 ANOVA (when the first variable is within subjects and the second between subjects). the effects are significant but the problem is that the variances are not equal (Levine test shows strong differences between the groups). Can somebody offer a solution (for example a specific kind of transformation that can make the variances equal) ? I will appreciate any help
Kelly Saporta, Ph.D. Department of Education and Psychology Email: [hidden email] http://www.openu.ac.il/Personal_sites/kelli-saporta/
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