FW: ANCOVA queries

[K F Pearce]

Hello everyone,

I would like to talk about 2 examples of ANCOVA . The examples which I
am looking at are from Brunig & Kintz (1987) "Computational Handbook of
Statistics pp205-222. Unfortunately the SPSS list does not allow me to
attach the data or annotated output and therefore I will have to
describe it.

For the first example, there is one dependent variable (SpellingY) and
one covariate (VocabX) and one (fixed)"factor" (method - with 3 levels).

 I am just checking that I am correctly understanding the way in which
SPSS is calculating the adjusted means.

After running:

UNIANOVA
  SpellingY  BY method  WITH VocabX
  /METHOD = SSTYPE(3)
  /INTERCEPT = INCLUDE
  /EMMEANS = TABLES(method) WITH(VocabX=MEAN)
  /PRINT = PARAMETER
  /CRITERIA = ALPHA(.05)
  /DESIGN = VocabX method .

the parameter estimates table reports coefficients as intercept=46.033,
VocabX=0.888, Method 1=-16.432, Method 2=5.542 and Method 3=0.

Am I correct that the 'estimate of the common slope'  is 0.888 as
extracted from the parameter estimates table and this is used in the
following equation [as 'slope'] to calculate the adjusted mean for each
level of the factor:

Hence for factor level j:
Adjusted mean j (for dept variable) =
observed mean (for dept variable) j - slope*(mean (for covariate) j -
grand mean of covariate)

The second example that I am studying has two (fixed) factors 'methods'
(2 levels) and 'times' (2 levels) and one covariate (AptX), there is one
dependent variable (Ratings Y). When testing that the homogeneity of
regression slopes asumption is met, Brunig & Kintz report a single F
statistic F=1.29/1.24=1.04. The only way that I can produce such a
statistic in SPSS is by creating another variable called 'Merge_Factor'
which has 4 levels associated with
1=(Method lev 1, Time lev 1), 2=(Method lev 2, Time lev 1), 3=(Method
lev 1, Time lev 2), 4=(Method lev 2, Time lev 2) and then running:

UNIANOVA
RatingsY BY Merge_Factor WITH AptX
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/CRITERIA = ALPHA(.05)
/DESIGN = Merge_Factor AptX AptX*Merge_Factor .

(we then look at the significance of the interaction term)

  Is this satisfactory to test that the homogeneity of regression slopes
assumptions is met for the 2 factor case?

Finally, does anyone have any references to good, clear examples which
detail what to do when the homogeneity of regression slopes assumption
is not met?

Thanks you so much for your help on these matters, Kind Regards, Kim

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[Juanito Talili]

Your post is very relevant.  Please share the comments when you receive offlist?

--- On Thu, 1/15/09, K F Pearce <[hidden email]> wrote:

From: K F Pearce <[hidden email]>
Subject: FW: ANCOVA queries
To: [hidden email]
Date: Thursday, 15 January, 2009, 2:26 PM

Hello everyone,

I would like to talk about 2 examples of ANCOVA . The examples which I
am looking at are from Brunig & Kintz (1987) "Computational Handbook
of
Statistics pp205-222. Unfortunately the SPSS list does not allow me to
attach the data or annotated output and therefore I will have to
describe it.

For the first example, there is one dependent variable (SpellingY) and
one covariate (VocabX) and one (fixed)"factor" (method - with 3
levels).

 I am just checking that I am correctly understanding the way in which
SPSS is calculating the adjusted means.

After running:

UNIANOVA
  SpellingY  BY method  WITH VocabX
  /METHOD = SSTYPE(3)
  /INTERCEPT = INCLUDE
  /EMMEANS = TABLES(method) WITH(VocabX=MEAN)
  /PRINT = PARAMETER
  /CRITERIA = ALPHA(.05)
  /DESIGN = VocabX method .

the parameter estimates table reports coefficients as intercept=46.033,
VocabX=0.888, Method 1=-16.432, Method 2=5.542 and Method 3=0.

Am I correct that the 'estimate of the common slope'  is 0.888 as
extracted from the parameter estimates table and this is used in the
following equation [as 'slope'] to calculate the adjusted mean for each
level of the factor:

Hence for factor level j:
Adjusted mean j (for dept variable) =
observed mean (for dept variable) j - slope*(mean (for covariate) j -
grand mean of covariate)

The second example that I am studying has two (fixed) factors 'methods'
(2 levels) and 'times' (2 levels) and one covariate (AptX), there is
one
dependent variable (Ratings Y). When testing that the homogeneity of
regression slopes asumption is met, Brunig & Kintz report a single F
statistic F=1.29/1.24=1.04. The only way that I can produce such a
statistic in SPSS is by creating another variable called 'Merge_Factor'
which has 4 levels associated with
1=(Method lev 1, Time lev 1), 2=(Method lev 2, Time lev 1), 3=(Method
lev 1, Time lev 2), 4=(Method lev 2, Time lev 2) and then running:

UNIANOVA
RatingsY BY Merge_Factor WITH AptX
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/CRITERIA = ALPHA(.05)
/DESIGN = Merge_Factor AptX AptX*Merge_Factor .

(we then look at the significance of the interaction term)

  Is this satisfactory to test that the homogeneity of regression slopes
assumptions is met for the 2 factor case?

Finally, does anyone have any references to good, clear examples which
detail what to do when the homogeneity of regression slopes assumption
is not met?

Thanks you so much for your help on these matters, Kind Regards, Kim

=====================
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