F Change in Hierarchical Regression

[Kate]

I am doing Hierarchical regression entering 3 variables at step one. I
don't get a significant F change for step one. But at step 2 when I
enter my variable of interest I do. However the overall F in the ANOVA
table for Model 2 is not significant. I don't understand this. I need to
report if the variable at step 2 made a significant contribution but I
confused.Do i report F change or the ANOVA F
Thanks
kate

[Rich Ulrich]

The ANOVA F is on all the variables in the model. Right?

But you have a "variable of interest" so what you want is the test on
that. It does not matter whether there were covariates before it that
accounted for 95% of the variance for a single score, or for 0.001% of
the variance with a dozen -- How should those affect the hypothesis?

(Well, they do shrink the error Sum of Squares, slightly. But they
don't dominate the test.) You need to have enough d.f. to have a
decent error term, but the test on your V. of I. has just the df
accounted for by the v. of i.

--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html

[jim clark]

Hi

> On Wed, 27 Sep 2000 14:05:50 +1000, Kate <ka...@onthenet.com.au> wrote:

At step 1, you have R^2y.234, which is not significant because
(SSreg/3)/(SSerr/(n-3-1)) with 3, n-3-1 df is not
significant. Note that it is _possible_ that 1 or more of the
predictors does make a significant contribution, but that the
effect is nonsignificant when diluted across all 3 predictors.

The same reasoning applies at the next step. Now you have
R^2y.1234, which is not sig, F = (SSreg/4)/(SSerr/(n-4-1)) with
4, n-4-1 df. But the unique contribution of one of the
predictors (e.g., x1) could (and is in your case)) be
significant.

The unique contribution of x1 is given by R^2change = R^2y.1234 -
R^2y.234 (or corresponding operations with SSreg's) and is tested
for significance by F = (SSchange/1)/(SSerr/(n-4-1))with 1, n-4-1
df. Note there is no dilution of the SSchange because it has a
single df. Fchange = t^2 for the significance of the regression
coefficent for x1, when x2, x3, and x4 are also in the equation.

Best wishes
Jim

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James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 cl...@uwinnipeg.ca
CANADA http://www.uwinnipeg.ca/~clark
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