Relationship between total slope, between slope, and within slope

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After studying Burstein (1980), Raudenbush and Bryk (2002), and Willms (2006), I'm trying to replicate the

beta-t = eta-squared (between-school slope) + (1 - eta-squared)(within-school slope)

relationship with a dummy variable (Asian) predicting math scores. I'm using NAEP 2003 math data, unweighted to keep it very simple. I've used SAS proc mixed and Mplus. I've ensured that all analyses are using the same cases by pre-deleting cases that are missing on the math score or on Asian. The total slope, based on the level 1 OLS regression, is 0.0532, but I can't find an eta-squared that produces a good match. I've tried, using proc univariate, the ratio

Sum of Squares (Asian) / Sum of Squares (grand-mean-centered Asian) =  0.378.

and, using proc mixed and an unconditional two-level model of Asian, the ratio
tau00/(tau00 + sigma-square) =  0.2705

These values do not lead exactly to a match for the total slope.
Does anyone have a tip?

NAEP Math Score predicted by ASIAN AT TWO LEVELS
UNWEIGHTED
R&B table 5.10
R&B Table 5.11
centering
None & group mean
Group mean
eta-sq (ss) based on sums of squares from proc univariate
0.378
0.378
eta-sq (res) based on tau00 and sigma-squared from an unconditional model using proc mixed
0.2705
0.2705
Between slope
-17.79
-16.673
Within slope
8.687
8.687
total slope, based on eta-sq (SS)
-1.3213
-0.8991
total slope, based on eta-sq (res)
1.5238
1.8260
Total slope, based on level 1 OLS regression
0.0532

• Burstein, Leigh. 1980. "The Analysis of Multilevel Data in Educational Research and Evaluation." Pp. 158-233 in Review of Research in Education, edited by D. C. Berliner: American Educational Research Association.
• Raudenbush, Stephen W. and Anthony Bryk. 2002. Hierarchical Linear Models: Applications and Data Analysis Methods. Thousand Oaks, CA: Sage.
• Willms, J. Douglas. 2006. "Learning Divides: Ten Policy Questions About the Performance and Equity of Schools and Schooling Systems." Vol.  UIS/WP/06-02. Montreal: UNESCO Institute for Statistics.
  

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关键词：relationship relations relation Between within

Hi.

I didn't get any responses to an earlier question; let me try to make it simpler.
Has anyone ever used SAS or Mplus to verify this equation from Raudenbush and Bryk (2002, equation 5.38)?

beta-t = eta-squared (between-school slope) + (1 - eta-squared)(within-school slope)

Where might I find the code that would do the job? I have tried with both packages and failed.
Maybe it's because my predictor variable is binary? Maybe I'm not using the right approach to find eta-squared? Maybe this is more of an approximation than an equation?

This equation is exact for balanced data. It is discussed, with a number of related equations, in Section 3.6 of T. Snijders & R. Bosker, "Multilevel Analysis: An introduction to Basic and Advanced Multilevel Modeling", 2nd edition, Sage, 2012; see equation (3.27). For non-balanced data there is a weighted version. The equation was first given (I believe) by Duncan, Curzort and Duncan, "Statistical Geography", Free Press, 1961.

Best wishes,
Tom A.B. Snijders
Professor of Statistics in the Social Sciences
University of Oxford
Professor of Statistics and Methodology
Department of Sociology