Differences between STAR (tm), BMDP (tm), and SPSS-X (tm). When data are
missing (unequal cell frequencies are present) STAR computes a complete Least
Squared Error solution (see Winer, 1971). To obtain the Least Squared Error
solution, STAR uses the computational steps outlined by Cohen and Cohen (1975,
1983). That is, STAR pairs the data with internally computed (or user
provided, as desired) dummy codings/coefficients, it computes the correlation
matrix from all the data, and then extracts all the sources of variance via
Hierarchical Multiple Regression.
Major differences between STAR and the other packages are highlighted. Note
that STAR displays the variance 'explained' by each source (R-Square). (All
displays are the result of 'default' processing, the displays have been
altered to facilitate comparison). Data from Winer (1971, page 801). SPSS and
BMDP are trade marks of SPSS Inc. and BMDP Inc., respectively.

STAR: Complete Least Squared Error Solution
--------------------------------------------------------------------------
***** STAR - Variance/Covariance/Trend Analysis ************
Design: A S B
Levels: 3 5 3
**************************************************************************
SOURCE R SQUARE MEAN SQUARE DEGREES OF F TAIL
FREEDOM PROB

A 0.018561 11.466669 2 0.168 0.848
ERROR 0.495827 68.069130 9

B 0.295459 182.527786 2 84.076 0.000
AB 0.158525 48.966671 4 22.555 0.000
ERROR 0.031628 2.170985 18
**************************************************************************
R square total = 1.00000 SS Total = 1235.556
--------------------------------------------------------------------------


BMDP (P2V program)
--------------------------------------------------------------------------
BMDP2V - ANALYSIS OF VARIANCE AND COVARIANCE WITH REPEATED MEASURES.

SOURCE SUM OF DEGREES OF MEAN F TAIL
SQUARES FREEDOM SQUARE PROB.
A 22.93333 2 11.46667 0.17 0.8476
ERROR 612.62222 9 68.06914

B 346.59598 2 173.29799 79.82 0.0000
AB 195.86667 4 48.96667 22.56 0.0000
ERROR 39.07778 18 2.17099
--------------------------------------------------------------------------


SPSS-X (MANOVA program)
--------------------------------------------------------------------------
Source of Variation SS DF MS F Sig of F
A 22.93 2 11.47 .17 .848
WITHIN CELLS 612.62 9 68.07

B 346.60 2 173.30 79.82 .000
AB 195.87 4 48.97 22.56 .000
WITHIN CELLS 39.08 18 2.17
--------------------------------------------------------------------------

STAR (tm), PC version: Part of Regression output. Data from Longley (1967,
JASA). Dependent variable is employment (Total). The output is shown in its
original form (the asterisk next to the partial correlation coefficient
indicates alpha <.05, the lower case 'a' indicates alpha <.10). This output is
produced for each stage in the regression.
Beta coefficients and intercept are identical to those reported by Longley
(1967) to as many decimal places as shown. Note the virtual identity of many
regression values between the output from STAR and the VAX (tm) version of
SPSS-X (tm) [beta, intercept, t-test value, probability of t, etc.]. The
difference between the two packages is one of emphasis. STAR concentrates
more on the display of variance accounted for or shared, e.g., semi-partial
square, partial square, variance in common between the independent variables
(X-X's R Square), partial correlation matrix, etc.
------------------------------------------------------------------------------
***** STAR - Hierarchical Multiple Regression, Double precision ********

******************************************************************************
STAGE: 1 # 'X' VARIABLES ENTERED: 6 TOTAL: 6

VARIABLES ENTERED: DEFLATOR, GNP, UNEMPLOY, SIZE AF, POPULAT, TIME.


PARTIAL CORRELATIONS MATRIX d.f. error = Ny-#V entered-1 = 9

DEFLATOR GNP UNEMPLOY SIZE AF POPULAT TIME
DEFLATOR -1.0000
GNP 0.6494* -1.0000
UNEMPLOY 0.5550a -0.9456* -1.0000
SIZE AF 0.3488 -0.4686 -0.6186* -1.0000
POPULAT -0.6592* 0.8332* 0.7583* 0.1889 -1.0000
TIME -0.1863 0.8017* 0.8241* 0.5494a -0.3882 -1.0000


VARIABLE RAW SEMI- S-PRTL TAIL S-PRTL PARTIAL X-X's
BETA PARTIAL t-TEST PROB SQUARE SQUARE R-SQUARE
DEFLATOR 15.0619 0.0040 0.177 .863 0.0000 0.0035 0.9926
GNP -0.0358 -0.0240 -1.070 .313 0.0006 0.1128 0.9994
UNEMPLOY -2.0202 -0.0927 -4.136 .003 0.0086 0.6553 0.9703
SIZE AF -1.0332 -0.1081 -4.822 .001 0.0117 0.7209 0.7214
POPULAT -0.0511 -0.0051 -0.226 .826 0.0000 0.0056 0.9975
TIME 1829.1515 0.0900 4.016 .003 0.0081 0.6418 0.9987


MULTIPLE R = 0.99774

SOURCE R SQUARE MEAN SQUARE DEGREES OF F TAIL
FREEDOM PROB

TOTAL 0.995479 30695400.324091 6 330.285 0.000
ERROR 0.004521 92936.006161 9

SHRUNKEN 0.992465 30602464.317930 6 197.571 0.000
ERROR 0.007535 154893.343602 9

INCREMENTAL 0.995479 30695400.324091 6 330.285 0.000
ERROR 0.004521 92936.006161 9
******************************************************************************
Y-INTERCEPT = -3482258.63459624

Part of regression output from the VAX (tm) version of SPSS-X (tm). Data from
Longley (1967, JASA). Dependent variable is Employment (Total). The output
has been altered to facilitate comparison with the output from STAR (the
'Analysis of variance' output has been moved to the bottom of the page and, in
addition to what is shown, the default output also includes the standardized
beta coefficient and the 95% confidence intervals for both standardized and
raw beta). The variables order was given to the package as it was for STAR.
However, SPSS-X 'decided' to rearrange the order of the variables to the one
shown.
-------------------------------------------------------------------------


* * * * M U L T I P L E R E G R E S S I O N * * * *

Variable(s) Entered on Step Number 1.. TIME
2.. SIZE AF
3.. UNEMPLOY
4.. DEFLATOR
5.. POPPULAT
6.. GNP

Multiple R .99774
R Square .99548 R Square Change .99548
Adjusted R Square .99247 F Change 330.28534
Standard Error 304.85407 Signif F Change .0000


-------------------- Variables in the Equation --------------------------
Variable B Correl Part Cor Partial Tolerance VIF

TIME 1829.151465 .971329 .090007 .801140 .001318 758.981
SIZE AF -1.033227 .457307 -.108074 -.849084 .278635 3.589
UNEMPLOY -2.020230 .502498 -.092709 -.809509 .029745 33.619
DEFLATOR 15.061872 .970899 .003975 .059022 .007378 135.532
POPULAT -.051104 .960391 -.005066 -.075137 .002505 399.151
GNP -.035819 .983552 -.023971 -.335804 5.591E-04 1788.513
(Constant) -3482258.635 890420.3836 -5496528.457 -1467988.813


Variable T Sig T

TIME 4.016 .0030
SIZE AF -4.822 .0009
UNEMPLOY -4.136 .0025
DEFLATOR .177 .8631
POPULAT -.226 .8262
GNP -1.070 .3127
(Constant) -3.911 .0036


Analysis of Variance
DF Sum of Squares Mean Square

Regression 6 184172401.94449 30695400.32408
Residual 9 836424.05551 92936.00617

F = 330.28534 Signif F = .0000


Part of the default regression output from the VAX (tm) version of BMDP (tm).
Data are from Longley (1967). Dependent variable is Employment. The output
has been slightly altered to make it fit on an 80 column display (the message
about variables not included has been moved to the left).

-----------------------------------------------------------------------------


BMDP1R - MULTIPLE LINEAR REGRESSION


MULTIPLE R 0.9927 STD. ERROR OF EST. 493.9479
MULTIPLE R-SQUARE 0.9855

ANALYSIS OF VARIANCE
SUM OF SQUARES DF MEAN SQUARE F RATIO P(TAIL)
REGRESSION 182324880.0000 4 45581220.0000 186.820 0.0000
RESIDUAL 2683830.2500 11 243984.5625

STD. STD. REG
VARIABLE COEFFICIENT ERROR COEFF T P(2 TAIL) TOLERANCE

INTERCEPT 50083.85547
DEFLATOR 2 56.2578 102.9398 0.17 0.55 0.60 0.0132
GNP 3 0.0353 0.0104 1.00 3.40 0.01 0.0153
UNEMPLOY 4 -0.8538 0.2434 -0.23 -3.51 0.00 0.3144
SIZE AF 5 -0.5495 0.2900 -0.11 -1.90 0.08 0.3995
POPULAT 6 VARIABLE NOT USED. TOLERANCE = 0.002950
TIME 7 VARIABLE NOT USED. TOLERANCE = 0.001551

NOTE - ONE OR MORE VARIABLES WERE NOT INCLUDED BECAUSE
THEIR INCLUSION WOULD REDUCE THE TOLERANCE OF AN
ALREADY INCLUDED VARIABLE BELOW THE TOLERANCE LIMIT