Date: Sat, 18 Jul 1998 02:12:05 -0500
Reply-To: "Nichols, David" <nichols@SPSS.COM>
Sender: "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From: "Nichols, David" <nichols@SPSS.COM>
Subject: Re: Still Anova-MCA
I could tell you how to compute the beta values in ANOVA, but not what a
reasonable interpretation of them is; you'd have to look at the original
MCA literature for that justification. They don't correspond to any
direct proportion of variance accounted for measure that I can see.
The partial eta^2 values in MANOVA for each term are that term's
hypothesis sum of squares divided by that plus the error sum of squares.
Thus, they don't add to the total R^2 for the model, even in balanced
data. In this case, you have unbalanced data (first, the unequal cell
sizes, second the covariates, which almost always introduce correlations
among the predictors), so there is no unique way to decompose the total
R^2 into additive pieces for each effect. The partial eta^2 values can
add up to more or less than the R^2, as can total eta^2 values, which
use the mean corrected total sum of squares in the denominators (and
would thus add to the total R^2 in a balanced situation). You can read
about some aspects of unbalanced data and contributions to R^2 in the
article ssnoadd.txt in http://www.spss.com/tech/Articles.html.
David Nichols
Principal Support Statistician and
Manager of Statistical Support
SPSS Inc.
>----------
>From: Pierre Mc Duff[SMTP:mcduffp@ERE.UMONTREAL.CA]
>Sent: Monday, July 06, 1998 7:00 PM
>To: SPSSX-L@UGA.CC.UGA.EDU
>Subject: Still Anova-MCA
>
>Hi,
>
>I'm still a bit confuse about the exact value of beta and Eta Squared in
>Anova and Manova. My problem is that one reviewer would like to know
>the
>contribution of each factor, specially in terms of explained variance.
>With the Anova procedure, I can see that the R2=.082, but if I look (in
>the Manova Output) at the contribution (partial Eta Squared) of the 2
>covariates, the 2 factors and the interaction, I'm far away from the
>.082. Am I missing something?
>
>Thanks for any help.
>
>
>4 anova depress by grfemale(1,4) intact(0,1) with edyrspmk ses
> 5 /sta=mca
> 6
>
>ANOVA problem requires 1392 bytes of memory.
>
> * * * A N A L Y S I S O F V A R I A N C E * * *
>
> DEPRESS
> by GRFEMALE Group of mothers
> INTACT Intact family
> with EDYRSPMK number of yrs of educ
> SES socio-economic status
>
>
> Sum of
>Mean Sig
>Source of Variation Squares DF Square
>F of F
>
>Covariates 16749.916 2 8374.958
>344.391 .000
> EDYRSPMK 68.885 1 68.885
>2.833 .092
> SES 7965.494 1 7965.494
>327.554 .000
>
>Main Effects 8389.186 4 2097.296
>86.244 .000
> GRFEMALE 973.402 3 324.467
>13.343 .000
> INTACT 6690.105 1 6690.105
>275.108 .000
>
>2-Way Interactions 105.784 3 35.261
>1.450 .226
> GRFEMALE INTACT 105.784 3 35.261
>1.450 .226
>
>Explained 25244.886 9 2804.987
>115.345 .000
>
>Residual 280461.046 11533 24.318
>
>Total 305705.932 11542 26.486
>
>
>12050 cases were processed.
>507 cases (4.2 pct) were missing.
>
>
> * * * M U L T I P L E C L A S S I F I C A T I O N A N A L Y S I S
>* * *
>
> DEPRESS
> by GRFEMALE
> INTACT
> with EDYRSPMK number of yrs of educ
> SES socio-economic status
>
>
>Grand Mean = 5.00 Adjusted for
> Independents
> Unadjusted + Covariates
>Variable + Category N Dev'n Eta Dev'n Beta
>
>GRFEMALE
> 1 2455 .06 -.12
> 2 5787 -.46 -.21
> 3 2882 .68 .44
> 4 419 1.31 .57
> .10 .06
>
>INTACT
> 0 8955 -.63 -.44
> 1 2588 2.18 1.54
> .23 .16
>
>Multiple R Squared .082
>Multiple R .287
>
>
>
>
>
>7 manova depress by grfemale(1,4) intact(0,1) with edyrspmk ses
> 8 /print=signif(efsize)/design
>
>* * * * * * A N A L Y S I S O F V A R I A N C E * * * * * *
>
>
> 11543 cases accepted.
> 0 cases rejected because of out-of-range factor values.
> 507 cases rejected because of missing data.
> 8 non-empty cells.
>
> 1 design will be processed.
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>-
>
>* * * * * * A N A L Y S I S O F V A R I A N C E -- DESIGN 1 * * *
>* * *
>
> Tests of Significance for DEPRESS using UNIQUE sums of squares
> Source of Variation SS DF MS F Sig of F
>
> WITHIN CELLS 280461.05 11533 24.32
> REGRESSION 7714.56 2 3857.28 158.62 .000
> GRFEMALE 531.86 3 177.29 7.29 .000
> INTACT 3532.22 1 3532.22 145.25 .000
> GRFEMALE BY INTACT 105.78 3 35.26 1.45 .226
>
>- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>-
> Effect Size Measures
> Partial
> Source of Variation ETA Sqd
>
> Regression .027
> GRFEMALE .002
> INTACT .012
> GRFEMALE BY INTACT .000
> Regression analysis for WITHIN CELLS error term
> --- Individual Univariate .9500 confidence intervals
> Dependent variable .. DEPRESS
>
> COVARIATE B Beta Std. Err. t-Value Sig. of t
>
> EDYRSPMK -.02117 -.00882 .034 -.626 .531
> SES -1.12111 -.15683 .101 -11.133 .000
>
> COVARIATE Lower -95% CL- Upper ETA Sq.
>
> EDYRSPMK -.087 .045 .000
> SES -1.318 -.924 .011
>
>
>7512 bytes of memory are needed for MANOVA execution.
>
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