Brown_Forsythe error in 1-way ANOVA?
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Brown_Forsythe error in 1-way ANOVA?
 
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Please help with this problem Most sources give same denominator df for Brown-Forsyth as for equal variance ANOVA Not SPSS, no idea how 170 for equal variance got reduced to 6.97 Furthermore, the Brown-Forsyth significance given by SPSS does not agree with either that corresponding to its own, now with that from df2 = N – k In this study, n1 =7, n2 = 165and there are 2 groups, K=2 Here are results: F df1 df2 sigSPSS sigdfA sigdfB predictor Equal variance .697 1 170 . 4051 .4051 predictor Brown-Forsythe .909 1 6.697 .3736 .3418 .3773 sigSPSS is significance in SPSS output SigdfA is significance using df = n1+n2 – k =7+165-2=170 SigdfB is significance using df in SPSS Brown-Forsyth Any ideas? Best Diana NB I know this is very unbalanced design, but problem occurs with more balanced designs. Nbt2 cited df is NOT the harmonic mean of n1, n2 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 |
Re: Brown_Forsythe error in 1-way ANOVA?
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Have you looked at the algorithms for Brown-Forsythe?
The d.f. calculation is fully spelled out there along with comments
about the validity of the approximation.
Jon Peck (no "h") aka Kim Senior Software Engineer, IBM [hidden email] phone: 720-342-5621 From: "Kornbrot, Diana" <[hidden email]> To: [hidden email], Date: 05/15/2013 04:09 AM Subject: [SPSSX-L] Brown_Forsythe error in 1-way ANOVA? Sent by: "SPSSX(r) Discussion" <[hidden email]> Dear SPSS experts Please help with this problem Most sources give same denominator df for Brown-Forsyth as for equal variance ANOVA Not SPSS, no idea how 170 for equal variance got reduced to 6.97 Furthermore, the Brown-Forsyth significance given by SPSS does not agree with either that corresponding to its own, now with that from df2 = N – k In this study, n1 =7, n2 = 165and there are 2 groups, K=2 Here are results: F df1 df2 sigSPSS sigdfA sigdfB predictor Equal variance .697 1 170 . 4051 .4051 predictor Brown-Forsythe .909 1 6.697 .3736 .3418 .3773 sigSPSS is significance in SPSS output SigdfA is significance using df = n1+n2 – k =7+165-2=170 SigdfB is significance using df in SPSS Brown-Forsyth Any ideas? Best Diana NB I know this is very unbalanced design, but problem occurs with more balanced designs. Nbt2 cited df is NOT the harmonic mean of n1, n2 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 |
Re: Brown_Forsythe error in 1-way ANOVA?
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In reply to this post by Kornbrot, Diana
Hi Diana:
Depending on how different the group variances are, BF degrees of freedom can get as low as the smallest sample df. Since you mention that n1=7 and n2=165, BF-df could perfectly be 6.697 (just above 6, the smallest sample df). You don't present the sample variances, but I'd bet that they are REALLY different. That' why I always recommend my students that, whenever possible, studies should be balanced. Only if the sample variances are really equal you will get BF-df close to n1+n2-2. Since you are comparing only 2 groups, use an independent samples t-test. The df for the different variances statistic should be close (I'd guess the same?) to the BF-df. HTH, Marta GG El 15/05/2013 12:08, Kornbrot, Diana escribió:
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Re: Brown_Forsythe error in 1-way ANOVA?
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In reply to this post by Kornbrot, Diana
There is a "Brown-Forsythe test" which is a test on whether
variances are equal. That one uses no reduction of d.f. That is not what you are looking at. I see where SPSS provides the Levene test on variances, but I don't see B-F, whether it is there or not. There is a Brown-Forsythe version of ANOVA which uses a correction to d.f. and a weighted computation of variance. That is what you are looking at. -- Rich Ulrich Date: Wed, 15 May 2013 11:08:24 +0100 From: [hidden email] Subject: Brown_Forsythe error in 1-way ANOVA? To: [hidden email] Please help with this problem Most sources give same denominator df for Brown-Forsyth as for equal variance ANOVA Not SPSS, no idea how 170 for equal variance got reduced to 6.97 Furthermore, the Brown-Forsyth significance given by SPSS does not agree with either that corresponding to its own, now with that from df2 = N – k In this study, n1 =7, n2 = 165and there are 2 groups, K=2 Here are results: F df1 df2 sigSPSS sigdfA sigdfB predictor Equal variance .697 1 170 . 4051 .4051 predictor Brown-Forsythe .909 1 6.697 .3736 .3418 .3773 sigSPSS is significance in SPSS output SigdfA is significance using df = n1+n2 – k =7+165-2=170 SigdfB is significance using df in SPSS Brown-Forsyth Any ideas? Best Diana NB I know this is very unbalanced design, but problem occurs with more balanced designs. Nbt2 cited df is NOT the harmonic mean of n1, n ... |
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Just to make things a little
clearer:
In the SPSS Algorithms for v20, there are
formulas for
the ONEWAY procedure that are provided for
the
Brown-Forsythe F test for means -- see
page 698-699.
This is the only Brown-Forsythe test in the
manual.
For those that have a copy of Gene Glass &
Kenneth Hopkins
3rd edition of Statistical Methods in Ed and
Psych, see their
chapter 15 for context and page 406 for
specifics on the
Brown-Forsythe F test for means.
Incidentally, G&H note that
when there are only two groups, the
Brown-Forsythe and the
Welch F are identical and equivalent which
implies that if the
Welch test is selected in ONEWAY, one should
get the equivalent
result.
Rich Ulrich mentions that there is a B-F test
for variances but this is
not available in SPSS. Glass &
Hopkins (3rd ed) cover it and its
relationships to other tests of homogeneity of
variance in section 16.10,
page 436-437.
As mentioned by Marta, the variances are
likely to be wildly different
and I assume that the skew and kurtosis are
very different as well,
which just makes the situation more
complicated.
-Mike Palij
New York University
----- Original Message -----
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Re: Brown_Forsythe error in 1-way ANOVA?
Administrator
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In reply to this post by Kornbrot, Diana
Diana, if you use ONEWAY's /MATRIX=OUT sub-command, you could share the data in a way that allows others to run the analysis for themselves (using /MATRIX = IN) to see what's going on. For example:
ONEWAY Y BY Group /STATISTICS BROWNFORSYTHE WELCH /MATRIX=OUT(*) . LIST. The resulting file has variables ROWTYPE_, Group, VARNAME_ and Y; and the row types are MEAN, STDDEV and N. (So if you post the data to let others run the analysis, you are posting summary statistics for the groups only, not raw data.) To run the same analysis with that dataset (rather than the raw data) as input: ONEWAY Y BY Group /STATISTICS BROWNFORSYTHE WELCH /MATRIX=IN(*) . HTH.
--
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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No time to examine closely, but this textbook demonstrates what appears to be a fairly straightforward way for conducting the B-F test in SPSS: The author (Andrew Hayes) goes on to state that this test is technically a test on "equality of dispersion." HTH. Ryan On Wed, May 15, 2013 at 2:25 PM, Bruce Weaver <[hidden email]> wrote: Diana, if you use ONEWAY's /MATRIX=OUT sub-command, you could share the data |
Re: Brown_Forsythe error in 1-way ANOVA?
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In Hotmail, I am seeing two threads with the same name.
Under the one with the original post, I posted the following - ***copied from earlier. There is a "Brown-Forsythe test" which is a test on whether variances are equal. That one uses no reduction of d.f. That is not what you are looking at. I see where SPSS provides the Levene test on variances, but I don't see B-F, whether it is there or not. There is a Brown-Forsythe version of ANOVA which uses a correction to d.f. and a weighted computation of variance. That is what you are looking at. ***end of copy. If that is not what explains the situation, then I am confused. -- Rich Ulrich Date: Wed, 15 May 2013 15:31:45 -0400 From: [hidden email] Subject: Re: Brown_Forsythe error in 1-way ANOVA? To: [hidden email] No time to examine closely, but this textbook demonstrates what appears to be a fairly straightforward way for conducting the B-F test in SPSS: The author (Andrew Hayes) goes on to state that this test is technically a test on "equality of dispersion." HTH. Ryan On Wed, May 15, 2013 at 2:25 PM, Bruce Weaver <[hidden email]> wrote: Diana, if you use ONEWAY's /MATRIX=OUT sub-command, you could share the data |
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In reply to this post by Ryan
Okay, this is getting out of hand. Ryan Black below cites a source
for
a Brown-Forsythe test of VARIANCES which does not appear in SPSS.
Just check any manual on algorithms. Black's source provides
equivalent
information to that Glass & Hopkins (3e) provide in their section
16.10 in
their chapter on "inferences about variances".
Since Diana Kornbrot has not been forthcoming with additional
details,
let me use some of my own data that seem to emulate her situation.
First, here are the descriptive statistics for a Reaction Time (RT)
difference
for the two groups in the variable "race.2": (Total N=177)
Report RT_diff race.2
Mean
N Std.
Deviation 0.00
202.8000
5
99.64788 1.00
194.1919
172
359.55507 Total
194.4350
177
354.73208 The standard deviation of Group1 is about 3.5 times that of Group 0.
Next, the ANOVA table:
ANOVA RT_diff ___________________SS____df____Mean
Square____F_____Sig. Between_______360.034_____1_______360.034___.003____.958 Within___22146573.469___175______26551.848
Finally, the Robust Tests of Equality of Means:
Robust Tests of Equality of
Means RT_diff ______________Statistica____df1_____df2___Sig. Welch___________.027_________1____7.575___.874 Brown-Forsythe__.027_________1____7.575___.874 a.
Asymptotically F distributed. Note that the df-Within from the ANOVA is 172 while df2 from
the Robust Means tests is 7.575 for both the Welch and Brown-Forsythe
tests. This, I believe, replicates the Kornbrot situation.
-Mike Palij
New York University
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Re: Brown_Forsythe error in 1-way ANOVA?
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Administrator
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If you wish to replicate Mike's analysis, run the following:
MATRIX DATA VARIABLES=Race ROWTYPE_ RT_diff /FACTORS=Race. BEGIN DATA 0 N 5 1 N 172 0 MEAN 202.8 1 MEAN 194.1919 0 STDDEV 99.64788 1 STDDEV 359.55507 END DATA. ONEWAY RT_diff BY Race /MATRIX=IN(*) /STATISTICS DESCRIPTIVES BROWNFORSYTHE WELCH . -------------------------------------------------------------- p.s. - Jon, the example of using MATRIX DATA with ONEWAY in the v20 FM shows ONEWAY specifying the range of values for the Group variable. I.e., ONEWAY WELL BY EDUC(1,6) /MATRIX=IN(*). When I tried that with the example shown above, it ran, but I got a warning message: Warnings Range specifications are no longer honored. All values have been used. To select a range of values, use the FILTER subcommand. It's not a big deal, but maybe something to add to the list of edits for the FM.
--
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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Just to add one little detail to what Bruce has provided below.
Previously, I had mentioned that Glass & Hopkins (3e) had pointed out that in the two group situation the Brown-Forsythe test for means and the Welch test are equivalent. This is confirmed by the ONEWAY output below but a further confirmation is provided by SPSS's t-test procedure. If one uses Bruce's syntax below, just add: t-test groups=race.2(0,1)/var=rt_diff. The "unequal variances" test is the Welch test though the FM does not mention this (for SPSS 20, algorithms manual, see pages 878-882). If one has a situation like Kornbrot's, one can use the t-test procedure instead of ONEWAY though SPSS does not make the connection. -Mike Palij New York University [hidden email] ----- Original Message ----- From: "Bruce Weaver" <[hidden email]> To: <[hidden email]> Sent: Wednesday, May 15, 2013 5:35 PM Subject: Re: Brown_Forsythe error in 1-way ANOVA? > If you wish to replicate Mike's analysis, run the following: > > MATRIX DATA VARIABLES=Race ROWTYPE_ RT_diff /FACTORS=Race. > BEGIN DATA > 0 N 5 > 1 N 172 > 0 MEAN 202.8 > 1 MEAN 194.1919 > 0 STDDEV 99.64788 > 1 STDDEV 359.55507 > END DATA. > > ONEWAY RT_diff BY Race > /MATRIX=IN(*) > /STATISTICS DESCRIPTIVES BROWNFORSYTHE WELCH > . > > -------------------------------------------------------------- > > p.s. - Jon, the example of using MATRIX DATA with ONEWAY in the v20 FM > shows > ONEWAY specifying the range of values for the Group variable. I.e., > > ONEWAY WELL BY EDUC*(1,6)* /MATRIX=IN(*). > > When I tried that with the example shown above, it ran, but I got a > warning > message: > > *Warnings* > Range specifications are no longer honored. All values have been used. To > select a range of values, use the FILTER subcommand. > > It's not a big deal, but maybe something to add to the list of edits for > the > FM. > > > > Mike Palij wrote >> Okay, this is getting out of hand. Ryan Black below cites a source for >> a Brown-Forsythe test of VARIANCES which does not appear in SPSS. >> Just check any manual on algorithms. Black's source provides equivalent >> information to that Glass & Hopkins (3e) provide in their section 16.10 >> in >> their chapter on "inferences about variances". >> >> Since Diana Kornbrot has not been forthcoming with additional details, >> let me use some of my own data that seem to emulate her situation. >> First, here are the descriptive statistics for a Reaction Time (RT) >> difference >> for the two groups in the variable "race.2": (Total N=177) >> >> Report >> >> RT_diff >> >> race.2 Mean N Std. Deviation >> >> 0.00 202.8000 5 99.64788 >> >> 1.00 194.1919 172 359.55507 >> >> Total 194.4350 177 354.73208 >> >> >> The standard deviation of Group1 is about 3.5 times that of Group 0. >> >> Next, the ANOVA table: >> >> ANOVA >> >> RT_diff >> >> ___________________SS____df____Mean Square____F_____Sig. >> >> Between_______360.034_____1_______360.034___.003____.958 >> >> Within___22146573.469___175______26551.848 >> >> Total_22146933.503 176 >> >> Finally, the Robust Tests of Equality of Means: >> >> Robust Tests of Equality of Means >> >> RT_diff >> >> ______________Statistica____df1_____df2___Sig. >> >> Welch___________.027_________1____7.575___.874 >> >> Brown-Forsythe__.027_________1____7.575___.874 >> >> a. Asymptotically F distributed. >> >> >> Note that the df-Within from the ANOVA is 172 while df2 from >> the Robust Means tests is 7.575 for both the Welch and Brown-Forsythe >> tests. This, I believe, replicates the Kornbrot situation. >> >> -Mike Palij >> New York University > >> mp26@ > >> >> ----- Original Message ----- >> From: Ryan Black >> To: > >> SPSSX-L@.UGA > >> >> Sent: Wednesday, May 15, 2013 3:31 PM >> Subject: Re: Brown_Forsythe error in 1-way ANOVA? >> >> >> No time to examine closely, but this textbook demonstrates what appears >> to be a fairly straightforward way for conducting the B-F test in SPSS: >> >> >> http://books.google.com/books?id=a-9m55d_uE0C&pg=PA226&lpg=PA226&dq=brown-forsythe+variance+test+spss&source=bl&ots=8DiDbHL4-D&sig=DBsbbzKMfDq8o6uScTphzJ1ZOak&hl=en&sa=X&ei=7t-TUaWqMvfe4APK8YCQBA&ved=0CD0Q6AEwAw#v=onepage&q=brown-forsythe%20variance%20test%20spss&f=false >> >> The author (Andrew Hayes) goes on to state that this test is >> technically >> a test on "equality of dispersion." >> >> HTH. >> >> Ryan >> >> >> >> >> On Wed, May 15, 2013 at 2:25 PM, Bruce Weaver < > >> bruce.weaver@ > >> > wrote: >> >> Diana, if you use ONEWAY's /MATRIX=OUT sub-command, you could share >> the data >> in a way that allows others to run the analysis for themselves (using >> /MATRIX = IN) to see what's going on. For example: >> >> ONEWAY Y BY Group >> /STATISTICS BROWNFORSYTHE WELCH >> /MATRIX=OUT(*) . >> LIST. >> >> The resulting file has variables ROWTYPE_, Group, VARNAME_ and Y; and >> the >> row types are MEAN, STDDEV and N. (So if you post the data to let >> others >> run the analysis, you are posting summary statistics for the groups >> only, >> not raw data.) >> >> To run the same analysis with that dataset (rather than the raw data) >> as >> input: >> >> ONEWAY Y BY Group >> /STATISTICS BROWNFORSYTHE WELCH >> /MATRIX=IN(*) . >> >> HTH. >> >> >> >> Kornbrot, Diana wrote >> >> > Dear SPSS experts >> > Please help with this problem >> > >> > Most sources give same denominator df for Brown-Forsyth as for >> equal >> > variance ANOVA >> > Not SPSS, no idea how 170 for equal variance got reduced to 6.97 >> > Furthermore, the Brown-Forsyth significance given by SPSS does not >> agree >> > with either that corresponding to its own, now with that from df2 = >> N - k >> > In this study, n1 =7, n2 = 165and there are 2 groups, K=2 >> > Here are results: >> > F df1 df2 >> > sigSPSS sigdfA sigdfB >> > predictor Equal variance .697 1 170 . 4051 >> .4051 >> > predictor Brown-Forsythe .909 1 6.697 .3736 >> .3418 >> > .3773 >> > >> > sigSPSS is significance in SPSS output >> > SigdfA is significance using df = n1+n2 - k =7+165-2=170 >> > SigdfB is significance using df in SPSS Brown-Forsyth >> > >> > Any ideas? >> > Best >> > Diana >> > >> > NB I know this is very unbalanced design, but problem occurs with >> more >> > balanced designs. >> > Nbt2 cited df is NOT the harmonic mean of n1, n2 >> > ________________________________ >> > Emeritus Professor Diana Kornbrot >> > email: >> >> >> > d.e.kornbrot@.ac >> >> >> > 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 >> >> >> >> >> >> >> ----- >> -- >> Bruce Weaver >> > >> bweaver@ > >> 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/Brown-Forsythe-error-in-1-way-ANOVA-tp5720253p5720264.html >> Sent from the SPSSX Discussion mailing list archive at Nabble.com. >> >> ===================== >> 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: > http://spssx-discussion.1045642.n5.nabble.com/Brown-Forsythe-error-in-1-way-ANOVA-tp5720253p5720269.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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In reply to this post by Mike
Apologies for any confusion I caused. My quick google search located a seemingly simple way using SPSS to employ the B-F test on, what is referred to as, equality in "dispersion." I posted it because there was discussion that there was no built in procedure for this test.
I was not referring to the B-F test on equality of means. Ryan On Wed, May 15, 2013 at 5:01 PM, Mike Palij <[hidden email]> wrote:
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In reply to this post by Bruce Weaver
Let's not leave the MIXED procedure out of this conversation! :-) The MIXED procedure can be used to test differences in means between k groups while accounting for heterogeneous variances, as shown below:
MIXED y BY group /FIXED=group | SSTYPE(3) /PRINT=SOLUTION /REPEATED=group | SUBJECT(subject) COVTYPE(DIAG). Ryan
On Wed, May 15, 2013 at 5:35 PM, Bruce Weaver <[hidden email]> wrote: If you wish to replicate Mike's analysis, run the following: |
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In reply to this post by Bruce Weaver
To be complete, it's probably worth the effort to just provide the actual df formula...Below is a demonstration of how to calculate df using Bruce's example: compute s1 = 99.64788. compute n1 = 5. compute s2 = 359.55507. compute n2 = 172. compute df = ((((s1**2) / n1) + ((s2)**2) / n2)**2) / ((s1**4) / ((n1**2)*(n1-1)) + (s2**4) / ((n2**2)*(n2-1))). execute. Ryan On Wed, May 15, 2013 at 5:35 PM, Bruce Weaver <[hidden email]> wrote: If you wish to replicate Mike's analysis, run the following: |
Re: Brown_Forsythe error in 1-way ANOVA?
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In reply to this post by Ryan
BUT it only works if the predictor is repeated Obviously, if all predictors are between there is no covariance matirx to calculate There could be unequal variances, but that option is not available Best Diana On 16/05/2013 00:34, "Ryan Black" <ryan.andrew.black@...> wrote: Let's not leave the MIXED procedure out of this conversation! :-) 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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I don't understand Diana Kornbrot's comments below. Using the
raw data that I used in ONEWAY and t-test and that Bruce
Weaver
uses below, first modify the syntax provided by Ryan Black to the
following:
MIXED rt_diff BY race.2
/FIXED=race.2 | SSTYPE(3) /PRINT=SOLUTION /REPEATED=race.2 | SUBJECT(userid) COVTYPE(DIAG). NOTE: race.2 is still a between-subjects factor and the existing
variable in the dataset "userid" uniquely identifies each
participant/subject.
The syntax runs without error and produces the following results
that are directly relevant:
The denominator df match those of the Brown-Forsythe and Welch
tests in ONEWAY and t-test (Welch only).
-Mike Palij
New York University
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In reply to this post by Kornbrot, Diana
Diana, This is not a "clever ploy." Your understanding of the diagonal covariance matrix I specified is incorrect. The model I specified tests for mean differences between k independent groups, while allowing for group-specific variances. Below is an illustration. Compare the test statistic, df, and p-value from B-F and WELCH's tests to the same statistics produced by the MIXED procedure. They are identical. Further, look at the covariance parameters estimated from the MIXED model. How do those group-specific variances compare to the group-specific variances calculated by EXAMINE VARIABLES? I'll tell you. They are identical.
Ryan *Generate data. set seed 98788978. new file. input program. loop subject= 1 to 100. if (subject>=1 or subject<=50) group=1. if (subject>50) group=2. compute y = 50*(group=1) + 45*(group=2) + sqrt(10)*rv.normal(0,1)*(group=1) + sqrt(20)*rv.normal(0,1)*(group=2). end case. end loop. end file. end input program. execute.
EXAMINE VARIABLES=y BY group /PLOT NONE /STATISTICS DESCRIPTIVES /CINTERVAL 95 /MISSING LISTWISE /NOTOTAL. ONEWAY y BY group
/STATISTICS BROWNFORSYTHE WELCH. MIXED y BY group /FIXED=group | SSTYPE(3) /REPEATED=group | SUBJECT(subject) COVTYPE(DIAG). On Thu, May 16, 2013 at 8:27 AM, Kornbrot, Diana <[hidden email]> wrote:
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Re: Brown_Forsythe error in 1-way ANOVA?
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In reply to this post by Mike
Context In psychology, education, consumer research etc ordinal variables with a small number of possible responses are very common,often with quite complex designs including repeated measure. Such data is almost always analysed using repeated measures ANOVA, on the grounds that ANOVA is robust to non-normality and they do not know of any alternative procedures anyway. I am testing this optimistic view with real data and SPSS, much used by my colleagues. Most existing tests use simulated data with non-normality features that may or may not resemble any set of real data. So part 1 is to compare PLUM with ANOVA, both using equal and unequal variance assumptions and also with Generalized Estimating Equations, GEE, as that is what one would need for a repeated measures design. Apologies about panic on df for Brown-Forsythe, SPSS is, of course, absolutely correct. Furthermore, there are references, but not ones that are easily avaialble on-line. Note to SPSS, think about that! The stated algorithm for df is correct. I found some misleading references with a quick google. EFFECT SIZES GLM is the only spss procedure that gives effect sizes direct. So I usually use partial eta-squared = Feffect*df1/(Feffect*df1 + df2), where df1 is for predictor effect and df2 is for error. df2 for this formula remains the same for unequal variance estimated of mean differences (N-k) MIXED ordinal procedures Was hoping to be able to a MIXED (repeated version of PLUM) Almost there: GEE gives same parameter values as PLUM with fixed scale. No option to use different scales.for different groups GEE only provides Wald chi square, not ML. GEE gives only parameters not Emeans. So parameters are always compared to last categroy. NO wy of specifying contrasts, e.g. Pairwise, which is what I wanted The DATA – for those interested See below for subset it took me time to extract. This is REAL data Subjects provide data in 8 conditions, indexed by strength, task, context. Data below is for just 1 condition. There are about 30 potential, predictors, I have supplied 2 predictors as an example. Please contact me off-line if you want more data Thanks again for everyone’s help Best Diana Subject Ordinal6Dependent Predictor1 Predictor2 5037 -1 -1 6104 6 -1 -1 4005 -1 -1 5065 -1 -1 8017 6 -1 -1 7010 6 -1 -1 8023 6 -1 -1 6008 6 -1 -1 6007 6 -1 -1 7033 6 -1 -1 4043 0 -1 -1 5073 6 -1 -1 4038 0 -1 -1 8010 0 -1 -1 6027 0 -1 -1 5019 6 -1 -1 7034 0 -1 -1 8019 6 -1 -1 8000 6 -1 -1 5006 6 -1 -1 5053 6 -1 -1 5014 6 -1 -1 6034 6 -1 -1 8005 6 -1 -1 8011 0 -1 -1 8013 6 -1 -1 5027 6 -1 -1 8022 6 -1 -1 5023 0 -1 -1 5005 6 -1 -1 5007 6 -1 -1 6047 0 -1 -1 8009 6 -1 -1 8014 6 -1 -1 4011 6 -1 -1 6009 6 -1 -1 6072 0 -1 -1 6030 6 -1 -1 8001 6 -1 -1 8002 6 -1 -1 8003 6 -1 -1 8004 6 -1 -1 8006 6 -1 -1 8007 6 -1 -1 8008 6 -1 -1 8012 6 -1 -1 8015 6 -1 -1 6024 6 -1 -1 8016 6 -1 -1 8018 6 -1 -1 6019 6 -1 -1 6002 6 -1 -1 8021 6 -1 -1 4022 6 -1 -1 7001 6 -1 -1 0430 0 0 0168 0 0 1055 0 1 1643 6 0 1 0107 0 1 2145 6 0 1 1124 0 0 1156 0 1 0143 6 0 0 1585 0 1 0422 0 0 0377 1 1 0479 0 0 1107 0 1 0296 0 1 1 1068 6 0 1 1375 6 0 0 1269 6 0 1 1662 6 0 1 0305 6 0 0 0044 2 0 0 0147 6 0 0 1016 6 0 0 2108 0 0 1 1631 0 1 1243 6 0 1 1092 0 1 2117 6 0 1 0434 0 0 0103 0 0 0 0473 0 1 1 2354 6 0 1 2130 4 0 0 1434 0 0 0 2218 6 0 0 1214 0 0 0 0203 6 0 0 2222 6 0 0 1621 0 0 0 1387 6 1 1 2464 0 0 0 1356 6 0 0 1407 6 0 1 0453 4 0 1 0318 0 0 1 2135 2 0 1 1187 4 0 0 1222 0 1 1 1741 6 0 0 0428 6 0 0 1024 6 0 0 0104 6 0 1 0010 0 0 0 2480 6 0 0 1595 6 0 0 0372 0 0 1 1235 0 0 1 1273 0 0 1 3054 6 0 0 2455 0 0 0 2466 2 0 1 0495 6 0 0 2379 6 0 0 0304 0 0 1174 0 1 2068 6 0 0 3022 6 0 0 2392 0 1 1694 0 1 1 0181 6 0 1 3081 0 0 1039 0 0 0 1216 6 0 1 2288 6 0 0 1364 6 0 1 1423 0 0 0261 0 1 1734 0 1 1298 6 0 0 1347 6 0 1 1341 0 0 1 1082 0 0012 6 0 1 1149 6 0 0 1264 0 0 0215 6 0 1 1025 0 0 0 1288 6 0 0 2115 6 0 0 2341 6 0 0 3013 6 0 0 0182 0 1 2104 6 0 1 2151 6 0 0 1062 6 0 0 0071 6 0 1 2221 0 0 1 3120 0 0 0 2351 6 0 0 3052 0 0 0 2034 6 0 0 0529 6 0 0 0191 6 0 1 1342 6 0 0 1308 6 0 0 2438 4 0 1 1127 0 0 1 1193 6 0 1 2140 6 0 1 2475 2 0 0 0291 6 0 0 2132 6 0 0 1206 0 0 0 3201 4 0 1 0413 6 0 0 3003 6 0 0 1061 6 0 0 2306 6 0 0 2164 6 0 1 2520 6 0 1 1599 6 0 0 0515 0 0 0 1324 0 0 0 2274 6 3126 6 0 1 0396 6 0 1 1052 6 0 0 2106 6 0 1 1184 0 0 1 2147 6 0 0 1209 0 0 0 3125 6 0 0 0309 0 0 1 2101 6 0 0 0230 0 0 1 2391 6 0 0 2182 6 0 0 2252 6 0 0 1558 6 0 0 1448 6 0 0 3092 6 0 0 1461 6 0 0 1180 6 0 1 2212 6 0 0 1310 6 0 0 1510 0 0 0 1027 6 0 0 1081 6 0 1 2169 6 0 0 1003 0 1 1 0524 6 0 1 3197 0 0 1 3152 6 0 0 1570 6 0 1 3068 0 0 0142 6 0 1 2122 0 0 1 0523 6 0 0 2146 6 0 1 0528 0 0 1 1369 6 0 0 2097 0 0 0 2186 6 0 0 1366 6 0 0 0194 6 0 1 2320 6 0 1 0276 4 0 0 1433 6 0 1 0005 6 0 1 1701 6 0 0 1711 6 0 0 2076 6 0 1 2304 6 0 1 0267 6 0 1 1268 6 0 0 2442 6 0 0 3175 6 0 0 2309 6 0 1 3024 6 0 1 2191 0 0 0 0257 6 0 0 2116 0 0 1 0355 0 0 0 0173 6 0 0 1443 6 0 0 1509 0 0 1 2196 0 0 0 1580 6 0 0 0408 0 0 0 1561 6 0 1 1095 0 0 1715 6 0 0 2005 6 0 1 2028 6 0 1 2386 6 0 1 1519 6 0 0 0439 6 0 0 2332 0 0 0 0491 6 0 1 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 |
Re: Brown_Forsythe error in 1-way ANOVA?
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Just to make your life
more complex. You might take a look at CATREG which allows you
to run the same data comparing results at different
levels of measurement.
Unfortunately we still have response scales with very few values. I believe this is somewhat a holdover from the days of counter-sorters where human effort was increased by having more values in a variable. In the extreme, this often has lead to researchers to commit the invidious median split. Although it happens less often in Ed and Psych many people represent a construct with a single item with very few categories. Art Kendall Social Research ConsultantsOn 5/16/2013 9:41 AM, Kornbrot, Diana [via SPSSX Discussion] wrote:
Art Kendall
Social Research Consultants |
Re: Brown_Forsythe error in 1-way ANOVA?
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Administrator
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In reply to this post by Ryan
Earlier this morning, before I saw Ryan's example below, I was working on one of my own in an attempt to understand the use of /REPEATED when there are no repeated measures. (That was a new one to me -- thanks for pointing it out, Ryan.)
For some reason, the denominator df from MIXED for my example do not equal the B-F df from ONEWAY. I can't see where I'm doing anything differently than in Ryan's example. Can anyone spot what the problem/difference is? (Maybe I should ask first if anyone can duplicate the results I get. I'm using v20 with patch running under Windoze 7.) * Modify the path below if necessary. GET FILE='C:\SPSSdata\1991 U.S. General Social Survey.sav'. ONEWAY age BY race /STATISTICS DESCRIPTIVES BROWNFORSYTHE WELCH . * Replicate the standard equal variances F-test via MIXED. MIXED age BY race /FIXED=race | SSTYPE(3) /PRINT=SOLUTION . * Now allow unequal variances via /REPEATED sub-command. COMPUTE subject = $casenum. MIXED age BY race /FIXED=race | SSTYPE(3) /PRINT=SOLUTION /REPEATED=race | SUBJECT(subject) COVTYPE(DIAG) . * B-F df2 from ONEWAY = 217.762 . * df2 from MIXED = 98.658 . * Why are they not the same?.
--
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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