Dear all
SPSS reports partial et-sq as opposed to eta-squared. I found in the literature the rule thumb for eta-squared as small (0.01), medium (0.06), and large (0.14) (Cohen, 1988). Does this apply to partial eta-squared as well? Also, the definition of eta-squared gives me the idea that it is no different than what some of us call partial R squared. Am I right? There is rumor out there that "researchers erroneously report partial eta-squared values as representing classical eta-squared values" http://carbon.cudenver.edu/~haguinis/APMinpress.pdf Any value in this argument? Thanx Enis |
see also
http://web.uccs.edu/lbecker/Psy590/es.htm and http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm On 7/18/06, Dogan, Enis <[hidden email]> wrote: > > Dear all > > > > SPSS reports partial et-sq as opposed to eta-squared. > > I found in the literature the rule thumb for eta-squared as small > (0.01), medium (0.06), and large (0.14) (Cohen, 1988). > > Does this apply to partial eta-squared as well? > > Also, the definition of eta-squared gives me the idea that it is no > different than what some of us call partial R squared. > > Am I right? > > > > There is rumor out there that "researchers erroneously report partial > eta-squared values as representing classical eta-squared values" > > http://carbon.cudenver.edu/~haguinis/APMinpress.pdf > > > > Any value in this argument? > > > > Thanx > > > > Enis > > > -- Alexander J. Shackman Laboratory for Affective Neuroscience Waisman Laboratory for Brain Imaging & Behavior University of Wisconsin-Madison 1202 West Johnson Street Madison, Wisconsin 53706 Telephone: +1 (608) 358-5025 FAX: +1 (608) 265-2875 EMAIL: [hidden email] http://psyphz.psych.wisc.edu/~shackman |
In reply to this post by Dogan, Enis
Just to clarify:
Cohen's rules of thumb that you list are for mean differences (t-tests, etc.) translated into r-sq. But his section on correlation uses small (r = .10, r-sq = .01), medium (r = .30, r-sq = .09), and large (r = .50, r-sq = .25). He then rectifies these discrepancies on pp. 81-82 (in the 1977 edition, sorry--don't have the '88 at hand, but the chapter on r). As to your question of partial et-sq and r-sq, I would be curious to any responses since I always assumed that the interpretation of the effect size of one would be equivalent to the other. Joe Burleson -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Dogan, Enis Sent: Tuesday, July 18, 2006 12:55 PM To: [hidden email] Subject: effect size: eta-squared vs partial eta-squared Dear all SPSS reports partial et-sq as opposed to eta-squared. I found in the literature the rule thumb for eta-squared as small (0.01), medium (0.06), and large (0.14) (Cohen, 1988). Does this apply to partial eta-squared as well? Also, the definition of eta-squared gives me the idea that it is no different than what some of us call partial R squared. Am I right? There is rumor out there that "researchers erroneously report partial eta-squared values as representing classical eta-squared values" http://carbon.cudenver.edu/~haguinis/APMinpress.pdf Any value in this argument? Thanx Enis |
In reply to this post by Dogan, Enis
A quick search on "eta" in the archives will confirm that some variant of
this question comes up pretty frequently! Unfortunately SPSS still has no capability to report total eta-squared values or the SS values needed to calculate total eta-squared values for mixed-model ANOVAs by hand (unless this functionality has since been added to SPSS 14/15). When Kyle Weeks last commented on this (Jan 2003 -- see http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0301&L=spssx-l&P=R2708&m=24876 ) he said this feature was on the "wish list" but I don't know if it has since become a reality. If someone knows of development or planned development on this it would be useful to know about it. Reporting partial eta-squared values would indeed be misleading given that when summed they can exceed 1. Unfortunately without SPSS reporting total eta-squared values it is likely that researchers do erroneously report partial values. Other articles on this include: Timothy R. Levine & Craig R. Hullett. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research, 28, 612-625. Pierce, C. A., Block, R. A., & Aguinis, H. (2004). Cautionary note on reporting eta-squared values from multifactor ANOVA designs. Educational and Psychological Measurement, 64, 916-924. http://www.montana.edu/wwwpy/Block/papers/Pierce,Block,&Aguinas-2004.pdf Nicholas Gibson -- Nicholas J.S. Gibson, Ph.D. Psychology and Religion Research Group Faculty of Divinity, University of Cambridge West Road, Cambridge, CB3 9BS, UK tel +44 (0)1223 763010 · mob +44 (0)7970 757524 · fax +44 (0)1223 763003 http://www.divinity.cam.ac.uk/pcp/personnel/nicholas.html > Date: Tue, 18 Jul 2006 12:01:26 -0500 > From: "Alexander J. Shackman" <[hidden email]> > > see also > > http://web.uccs.edu/lbecker/Psy590/es.htm > and > http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm > > On 7/18/06, Dogan, Enis <[hidden email]> wrote: > > > > Dear all > > > > > > > > SPSS reports partial et-sq as opposed to eta-squared. > > > > I found in the literature the rule thumb for eta-squared as small > > (0.01), medium (0.06), and large (0.14) (Cohen, 1988). > > > > Does this apply to partial eta-squared as well? > > > > Also, the definition of eta-squared gives me the idea that it is no > > different than what some of us call partial R squared. > > > > Am I right? > > > > > > > > There is rumor out there that "researchers erroneously report partial > > eta-squared values as representing classical eta-squared values" > > > > http://carbon.cudenver.edu/~haguinis/APMinpress.pdf > > > > > > > > Any value in this argument? > > > > > > > > Thanx > > > > > > > > Enis > > > > > > > > |
In reply to this post by Dogan, Enis
Thanks to all who replied to my question.
Any comments on the relationship between partial-eta squared and partial R squared? Also eta-squared looks to me like a part R squared. Any thoughts? Enis -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Nicholas J.S. Gibson Sent: Wednesday, July 19, 2006 12:37 PM To: [hidden email] Subject: Re: effect size: eta-squared vs partial eta-squared A quick search on "eta" in the archives will confirm that some variant of this question comes up pretty frequently! Unfortunately SPSS still has no capability to report total eta-squared values or the SS values needed to calculate total eta-squared values for mixed-model ANOVAs by hand (unless this functionality has since been added to SPSS 14/15). When Kyle Weeks last commented on this (Jan 2003 -- see http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0301&L=spssx-l&P=R2708&m=24 876 ) he said this feature was on the "wish list" but I don't know if it has since become a reality. If someone knows of development or planned development on this it would be useful to know about it. Reporting partial eta-squared values would indeed be misleading given that when summed they can exceed 1. Unfortunately without SPSS reporting total eta-squared values it is likely that researchers do erroneously report partial values. Other articles on this include: Timothy R. Levine & Craig R. Hullett. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research, 28, 612-625. Pierce, C. A., Block, R. A., & Aguinis, H. (2004). Cautionary note on reporting eta-squared values from multifactor ANOVA designs. Educational and Psychological Measurement, 64, 916-924. http://www.montana.edu/wwwpy/Block/papers/Pierce,Block,&Aguinas-2004.pdf Nicholas Gibson -- Nicholas J.S. Gibson, Ph.D. Psychology and Religion Research Group Faculty of Divinity, University of Cambridge West Road, Cambridge, CB3 9BS, UK tel +44 (0)1223 763010 * mob +44 (0)7970 757524 * fax +44 (0)1223 763003 http://www.divinity.cam.ac.uk/pcp/personnel/nicholas.html > Date: Tue, 18 Jul 2006 12:01:26 -0500 > From: "Alexander J. Shackman" <[hidden email]> > > see also > > http://web.uccs.edu/lbecker/Psy590/es.htm > and > http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm > > On 7/18/06, Dogan, Enis <[hidden email]> wrote: > > > > Dear all > > > > > > > > SPSS reports partial et-sq as opposed to eta-squared. > > > > I found in the literature the rule thumb for eta-squared as small > > (0.01), medium (0.06), and large (0.14) (Cohen, 1988). > > > > Does this apply to partial eta-squared as well? > > > > Also, the definition of eta-squared gives me the idea that it is no > > different than what some of us call partial R squared. > > > > Am I right? > > > > > > > > There is rumor out there that "researchers erroneously report > > eta-squared values as representing classical eta-squared values" > > > > http://carbon.cudenver.edu/~haguinis/APMinpress.pdf > > > > > > > > Any value in this argument? > > > > > > > > Thanx > > > > > > > > Enis > > > > > > > > |
Enis, in Keppel and Wickens (2004) the authors make a rather compelling argument against the R^2 effect size as reported in SPSS (i.e, SSa/SStotal) as opposed to omega squared, using their notation on page 164: (SSa - (a -1)MS s/a)/(SStotal + MS s/a)..they comment that omega squared "takes the sampling variability into account and so is most relevant to the population you are studying" (p. 167) and that, in their opinion, r^2 (which statistically can be shown) tends to inflate the variation accounted for.....however, SPSS does not report omega squared so one would need to hand calculate this estimate
Keppel, G., & Wickens, T. D. (2004). Design and analysis. (4th Ed.). Upper Saddle River, NJ: Pearson. "Dogan, Enis" <[hidden email]> wrote: Thanks to all who replied to my question. Any comments on the relationship between partial-eta squared and partial R squared? Also eta-squared looks to me like a part R squared. Any thoughts? Enis -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Nicholas J.S. Gibson Sent: Wednesday, July 19, 2006 12:37 PM To: [hidden email] Subject: Re: effect size: eta-squared vs partial eta-squared A quick search on "eta" in the archives will confirm that some variant of this question comes up pretty frequently! Unfortunately SPSS still has no capability to report total eta-squared values or the SS values needed to calculate total eta-squared values for mixed-model ANOVAs by hand (unless this functionality has since been added to SPSS 14/15). When Kyle Weeks last commented on this (Jan 2003 -- see http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0301&L=spssx-l&P=R2708&m=24 876 ) he said this feature was on the "wish list" but I don't know if it has since become a reality. If someone knows of development or planned development on this it would be useful to know about it. Reporting partial eta-squared values would indeed be misleading given that when summed they can exceed 1. Unfortunately without SPSS reporting total eta-squared values it is likely that researchers do erroneously report partial values. Other articles on this include: Timothy R. Levine & Craig R. Hullett. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research, 28, 612-625. Pierce, C. A., Block, R. A., & Aguinis, H. (2004). Cautionary note on reporting eta-squared values from multifactor ANOVA designs. Educational and Psychological Measurement, 64, 916-924. http://www.montana.edu/wwwpy/Block/papers/Pierce,Block,&Aguinas-2004.pdf Nicholas Gibson -- Nicholas J.S. Gibson, Ph.D. Psychology and Religion Research Group Faculty of Divinity, University of Cambridge West Road, Cambridge, CB3 9BS, UK tel +44 (0)1223 763010 * mob +44 (0)7970 757524 * fax +44 (0)1223 763003 http://www.divinity.cam.ac.uk/pcp/personnel/nicholas.html > Date: Tue, 18 Jul 2006 12:01:26 -0500 > From: "Alexander J. Shackman" > > see also > > http://web.uccs.edu/lbecker/Psy590/es.htm > and > http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm > > On 7/18/06, Dogan, Enis wrote: > > > > Dear all > > > > > > > > SPSS reports partial et-sq as opposed to eta-squared. > > > > I found in the literature the rule thumb for eta-squared as small > > (0.01), medium (0.06), and large (0.14) (Cohen, 1988). > > > > Does this apply to partial eta-squared as well? > > > > Also, the definition of eta-squared gives me the idea that it is no > > different than what some of us call partial R squared. > > > > Am I right? > > > > > > > > There is rumor out there that "researchers erroneously report > > eta-squared values as representing classical eta-squared values" > > > > http://carbon.cudenver.edu/~haguinis/APMinpress.pdf > > > > > > > > Any value in this argument? > > > > > > > > Thanx > > > > > > > > Enis > > > > > > > > Dale Glaser, Ph.D. Principal--Glaser Consulting Lecturer--SDSU/USD/CSUSM/AIU 4003 Goldfinch St, Suite G San Diego, CA 92103 phone: 619-220-0602 fax: 619-220-0412 email: [hidden email] website: www.glaserconsult.com |
Hi
DG> Enis, in Keppel and Wickens (2004) the authors make a rather DG> compelling argument against the R^2 effect size as reported in DG> SPSS (i.e, SSa/SStotal) as opposed to omega squared, using their DG> notation on page 164: (SSa - (a -1)MS s/a)/(SStotal + MS DG> s/a)..they comment that omega squared "takes the sampling DG> variability into account and so is most relevant to the population DG> you are studying" (p. 167) and that, in their opinion, r^2 (which DG> statistically can be shown) tends to inflate the variation DG> accounted for.....however, SPSS does not report omega squared so DG> one would need to hand calculate this estimate DG> Keppel, G., & Wickens, T. D. (2004). Design and analysis. DG> (4th Ed.). Upper Saddle River, NJ: Pearson. My contribution: * See http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm *. * Example dataset *. DATA LIST FREE/iv(F8.0) dv(F8.1). BEGIN DATA 1 7.5 1 6.2 1 6.9 1 7.4 1 9.2 1 8.3 1 7.6 2 5.8 2 7.3 2 8.2 2 7.1 2 7.8 2 7.2 2 7.3 3 5.9 3 6.2 3 5.8 3 4.7 3 7.3 3 7.2 3 6.2 4 6.2 4 6.8 4 5.7 4 4.9 4 6.2 4 5.8 4 5.4 END DATA. VALUE LABEL iv 1'NonSmoker' 2'ExSmoker' 3'Smoke<1' 4'Smoke>1'. VAR LABEL iv 'Smoking status during pregnancy' dv'Baby weight (pounds)'. MATRIX. PRINT /TITLE='OMEGA-SQUARE & ETA-SQUARE IN ONEWAY ANOVA'. GET data /VAR = iv dv /MISSING = OMIT. COMPUTE n = CSUM(DESIGN(data(:,1))). COMPUTE k = NCOL(n). COMPUTE kn=NROW(data). COMPUTE gsum = T(data(:,2))*DESIGN(data(:,1)). COMPUTE gsum2= T(data(:,2)&**2)*DESIGN(data(:,1)). COMPUTE mean = gsum/n. COMPUTE variance = (gsum2-(gsum&**2)/n)/(n-1). COMPUTE Iroof = RSUM(gsum2). COMPUTE Aroof = RSUM((gsum&**2)/n). COMPUTE Troof = (RSUM(gsum))&**2/kn. COMPUTE SSE = Aroof - Troof. COMPUTE MSE = SSE/(k-1). COMPUTE SSw = Iroof - Aroof. COMPUTE MSw = SSw/(kn-k). COMPUTE SST = Iroof - Troof. COMPUTE Ftest = MSE/MSw. COMPUTE Fsig = (1-FCDF(Ftest,k-1,kn-k)). COMPUTE omega2 = (SSE - (k-1)*MSw)/(SST+MSw). COMPUTE eta2 = SSE/SST. COMPUTE meann = k/MSUM(1/n). COMPUTE fvalue=SQRT(Ftest/meann). PRINT {T(mean),T(SQRT(variance)),T(n)} /FORMAT='F8.2' /CLABEL='Mean','SD','N' /RLABEL='No fuma','Ex-Fuma','Fuma<1','Fuma>1' /TITLE='Descriptive statistics'. PRINT {Ftest,Fsig} /FORMAT='F8.4' /CLABEL='F','Sig.' /TITLE='ANOVA test'. PRINT {eta2;omega2;fvalue} /FORMAT='F8.3' /RLABEL='Eta²','Omega²','f' /TITLE='Measures of effect size for ONEWAY ANOVA'. END MATRIX. * Using UNIANOVA *. UNIANOVA dv BY iv /PRINT = DESCRIPTIVE ETASQ /DESIGN = iv . * Example dataset *. DATA LIST LIST/control zone1 zone2 zone3. BEGIN DATA 15.0 17.9 16.5 16.7 23.5 26.5 35.4 34.1 20.1 45.2 22.6 20.2 26.1 39.1 33.4 30.6 26.5 35.2 37.6 30.1 19.4 35.1 30.4 24.6 16.4 31.8 23.2 20.1 21.1 21.4 20.8 18.4 19.8 33.1 29.4 24.3 17.4 31.1 28.4 29.6 END DATA. MATRIX. PRINT /TITLE='OMEGA-SQUARE, ETA-SQUARE & PARTIAL ETA-SQUARE FOR RM ANOVA'. GET data /VAR=ALL /NAME=gnames. COMPUTE b = NROW(data). COMPUTE k = NCOL(data). COMPUTE Iroof = MSSQ(data). COMPUTE Aroof = RSUM((CSUM(data))&**2/b). COMPUTE Broof = CSUM((RSUM(data))&**2/k). COMPUTE Troof = (MSUM(data)&**2)/(b*k). COMPUTE SSE = Aroof - Troof. COMPUTE MSE = SSE/(k-1). COMPUTE SSB = Broof - Troof. COMPUTE SST = Iroof - Troof. COMPUTE SSw = SST - SSE - SSB. COMPUTE MSw = SSE/((b-1)*(k-1)). COMPUTE Ftest = MSE/MSw. COMPUTE Fsig = (1-FCDF(Ftest,k-1,(k-1)*(b-1))). COMPUTE omega2 = (SSE - (k-1)*MSw)/(SST+MSw). COMPUTE eta2 = SSE/SST. COMPUTE pareta2 = SSE/(SSE+SSw). PRINT {CSUM(data)/b;SQRT((CSSQ(data)-(CSUM(data)&**2/b))/(b-1))} /FORMAT='F8.4' /CNAMES=gnames /RLABEL='Mean','SD' /TITLE='Descriptive statistics'. PRINT {Ftest,Fsig} /FORMAT='F8.4' /CLABEL='F','Sig.' /TITLE='ANOVA for Within Subjects Factor'. PRINT {omega2;eta2;pareta2} /FORMAT='F8.4' /RLABEL='Omega²','Eta²','Eta²Part' /TITLE='Measures of effect size for Within Subjects Factor'. END MATRIX. * Using UNIANOVA *. VARSTOCASES /ID = id /MAKE trans1 FROM control zone1 zone2 zone3 /INDEX = index1(trans1) /KEEP = /NULL = KEEP. UNIANOVA trans1 BY index1 id /RANDOM = id /METHOD = SSTYPE(3) /INTERCEPT = EXCLUDE /PRINT = ETASQ /DESIGN = index1 id . Closing time here in Spain... See you tomorrow. |
I have a multilevel dataset with quite a few singletons, i.e, level one units with n = 1; I believe that all of the level 2 units will be kept for the fixed effects analysis, but this would not be the case for the estimation of the variance components. A colleague commented that in regards to SAS MIXED....."SAS probably addresses this issue by excluding "effects" (which are confounded across levels) when estimating sample- and group-level variances". However, I use SPSS mixed model and HLM6.0 and I wanted to see if anyone on this listserv knew if SPSS and/or HLM handle singletons (n =1 at level 1) statistically in the same way as SAS?....thank you very much for any help......Dale
Dale Glaser, Ph.D. Principal--Glaser Consulting Lecturer--SDSU/USD/CSUSM/AIU 4003 Goldfinch St, Suite G San Diego, CA 92103 phone: 619-220-0602 fax: 619-220-0412 email: [hidden email] website: www.glaserconsult.com |
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