repeated measures custom contrasts for linear trends

[Paul Mcgeoghan]

Hi,

I have a customer with a within-subject factor (MOVES) with 10 levels and a between subject factor
with 3 levels (IAC).

He wants to test if there is a linear trend at each of the 3 between subject factor levels.

What would be the syntax for this?

I currently have the syntax below:

GLM
  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY iac
  /WSFACTOR = trial 10 Polynomial
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(trial) COMPARE ADJ(BONFERRONI)
 /EMMEANS = TABLES(iac*trial) COMPARE(iac) ADJ(bonferroni)
 /EMMEANS = TABLES(iac*trial) COMPARE(trial) ADJ(bonferroni)
  /PRINT = DESCRIPTIVE
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = trial
  /DESIGN = iac .

Thanks,
Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

[statisticsdoc]

Paul,

Do you have a significant interaction between MOVES and IAC (i.e., is there
evidence that the slope of the within-subject factor varies as a function of
the between-subject factor)?

Best,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Paul Mcgeoghan
Sent: Monday, February 05, 2007 6:02 AM
To: [hidden email]
Subject: repeated measures custom contrasts for linear trends


Hi,

I have a customer with a within-subject factor (MOVES) with 10 levels and a
between subject factor
with 3 levels (IAC).

He wants to test if there is a linear trend at each of the 3 between subject
factor levels.

What would be the syntax for this?

I currently have the syntax below:

GLM
  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY
iac
  /WSFACTOR = trial 10 Polynomial
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(trial) COMPARE ADJ(BONFERRONI)
 /EMMEANS = TABLES(iac*trial) COMPARE(iac) ADJ(bonferroni)
 /EMMEANS = TABLES(iac*trial) COMPARE(trial) ADJ(bonferroni)
  /PRINT = DESCRIPTIVE
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = trial
  /DESIGN = iac .

Thanks,
Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

[Paul Mcgeoghan]

Stephen,

The Tests of Within-Subjects effects Greenhouse-Geisser is significant .040 and Huynh-Feldt is
significant .027 for the MOVES*IAC interaction.

The Tests of Within Subjects Contrasts indicates a significant cubic effect (.039) for MOVES*IAC.

So yes.

Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

>>> "Statisticsdoc" <[hidden email]> 05/02/2007 13:17:56 >>>
Paul,

Do you have a significant interaction between MOVES and IAC (i.e., is there
evidence that the slope of the within-subject factor varies as a function of
the between-subject factor)?

Best,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Paul Mcgeoghan
Sent: Monday, February 05, 2007 6:02 AM
To: [hidden email]
Subject: repeated measures custom contrasts for linear trends


Hi,

I have a customer with a within-subject factor (MOVES) with 10 levels and a
between subject factor
with 3 levels (IAC).

He wants to test if there is a linear trend at each of the 3 between subject
factor levels.

What would be the syntax for this?

I currently have the syntax below:

GLM
  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY
iac
  /WSFACTOR = trial 10 Polynomial
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(trial) COMPARE ADJ(BONFERRONI)
 /EMMEANS = TABLES(iac*trial) COMPARE(iac) ADJ(bonferroni)
 /EMMEANS = TABLES(iac*trial) COMPARE(trial) ADJ(bonferroni)
  /PRINT = DESCRIPTIVE
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = trial
  /DESIGN = iac .

Thanks,
Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

[statisticsdoc]

Paul,

Replace Polynomial with Special in the WSFACTOR line, and supply a set of
contrasts that you specify.  Since you have a significant cubic interaction,
you should consider more than just the linear trend.  Testing just the
linear trend might be misleading if there are cubic or other higher order
effects.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Paul Mcgeoghan
Sent: Monday, February 05, 2007 8:27 AM
To: [hidden email]
Subject: Re: repeated measures custom contrasts for linear trends


Stephen,

The Tests of Within-Subjects effects Greenhouse-Geisser is significant .040
and Huynh-Feldt is
significant .027 for the MOVES*IAC interaction.

The Tests of Within Subjects Contrasts indicates a significant cubic effect
(.039) for MOVES*IAC.

So yes.

Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

>>> "Statisticsdoc" <[hidden email]> 05/02/2007 13:17:56 >>>
Paul,

Do you have a significant interaction between MOVES and IAC (i.e., is there
evidence that the slope of the within-subject factor varies as a function of
the between-subject factor)?

Best,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Paul Mcgeoghan
Sent: Monday, February 05, 2007 6:02 AM
To: [hidden email]
Subject: repeated measures custom contrasts for linear trends


Hi,

I have a customer with a within-subject factor (MOVES) with 10 levels and a
between subject factor
with 3 levels (IAC).

He wants to test if there is a linear trend at each of the 3 between subject
factor levels.

What would be the syntax for this?

I currently have the syntax below:

GLM
  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY
iac
  /WSFACTOR = trial 10 Polynomial
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(trial) COMPARE ADJ(BONFERRONI)
 /EMMEANS = TABLES(iac*trial) COMPARE(iac) ADJ(bonferroni)
 /EMMEANS = TABLES(iac*trial) COMPARE(trial) ADJ(bonferroni)
  /PRINT = DESCRIPTIVE
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = trial
  /DESIGN = iac .

Thanks,
Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

[Paul Mcgeoghan]

On Mon, 5 Feb 2007 09:08:35 -0500, Statisticsdoc <[hidden email]>
wrote:

>Paul,
>
>Replace Polynomial with Special in the WSFACTOR line, and supply a set of
>contrasts that you specify.  Since you have a significant cubic
interaction,

>you should consider more than just the linear trend.  Testing just the
>linear trend might be misleading if there are cubic or other higher order
>effects.
>
>HTH,
>
>Stephen Brand
>
>For personalized and professional consultation in statistics and research
>design, visit
>www.statisticsdoc.com
>
>
>-----Original Message-----
>From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
>Paul Mcgeoghan
>Sent: Monday, February 05, 2007 8:27 AM
>To: [hidden email]
>Subject: Re: repeated measures custom contrasts for linear trends
>
>
>Stephen,
>
>The Tests of Within-Subjects effects Greenhouse-Geisser is significant .040
>and Huynh-Feldt is
>significant .027 for the MOVES*IAC interaction.
>
>The Tests of Within Subjects Contrasts indicates a significant cubic effect
>(.039) for MOVES*IAC.
>
>So yes.
>
>Paul
>
>
>==================
>Paul McGeoghan,
>Application support specialist (Statistics and Databases),
>University Infrastructure Group (UIG),
>Information Services,
>Cardiff University.
>Tel. 02920 (875035).
>
>>>> "Statisticsdoc" <[hidden email]> 05/02/2007 13:17:56 >>>
>Paul,
>
>Do you have a significant interaction between MOVES and IAC (i.e., is there
>evidence that the slope of the within-subject factor varies as a function

of

>the between-subject factor)?
>
>Best,
>
>Stephen Brand
>
>For personalized and professional consultation in statistics and research
>design, visit
>www.statisticsdoc.com
>
>
>-----Original Message-----
>From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
>Paul Mcgeoghan
>Sent: Monday, February 05, 2007 6:02 AM
>To: [hidden email]
>Subject: repeated measures custom contrasts for linear trends
>
>
>Hi,
>
>I have a customer with a within-subject factor (MOVES) with 10 levels and a
>between subject factor
>with 3 levels (IAC).
>
>He wants to test if there is a linear trend at each of the 3 between

subject

>factor levels.
>
>What would be the syntax for this?
>
>I currently have the syntax below:
>
>GLM
>  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY
>iac
>  /WSFACTOR = trial 10 Polynomial
>  /METHOD = SSTYPE(3)
>  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
>  /EMMEANS = TABLES(trial) COMPARE ADJ(BONFERRONI)
> /EMMEANS = TABLES(iac*trial) COMPARE(iac) ADJ(bonferroni)
> /EMMEANS = TABLES(iac*trial) COMPARE(trial) ADJ(bonferroni)
>  /PRINT = DESCRIPTIVE
>  /CRITERIA = ALPHA(.05)
>  /WSDESIGN = trial
>  /DESIGN = iac .
>
>Thanks,
>Paul
>
>
>==================
>Paul McGeoghan,
>Application support specialist (Statistics and Databases),
>University Infrastructure Group (UIG),
>Information Services,
>Cardiff University.
>Tel. 02920 (875035).

Hi,

Having found that a cubic interaction exists between the within subject
factor MOVES and the between subject factor IAC, I click on Options and
Transformation Matrix.

This gives me the M matrix in the output (taking the coefficients from
that) and using the L matrix below will allow me to look at whether there
is a linear, quadratic or cubic trend at each individual Between Subject
Factor level.

Is this correct syntax and if not, what is the syntax to use?

GLM
  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY
iac
  /WSFACTOR = moves 10 Polynomial
/lmatrix 'Nesting within iac(1)' all 1 1 0 0
/lmatrix 'Nesting within iac(2)' all 1 0 1 0
/lmatrix 'Nesting within iac(3)' all 1 0 0 1
/mmatrix 'Linear trend using normalized metric'
all -.495 -.385 -.275 -.165 -.055 .055 .165 .275 .385 .495;
'Quadratic trend using normalized metric'
all .522 .174 -.087 -.261 -.348 -.348 -.261 -.087 .174 .522;
'Cubic trend using normalized metric'
all -.453 .151 .378 .335 .130 -.130 -.335 -.378 -.151 .453
  /CONTRAST (iac)=Polynomial
  /METHOD = SSTYPE(3)
  /PLOT = PROFILE( moves*iac )
  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(moves) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(iac*moves)
  /PRINT = TEST(MMATRIX)
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = moves
  /DESIGN = iac .

[Richard Ristow]

I realized this has been tickling at the back of my skull since you
posted it.

At 08:27 AM 2/5/2007, Paul Mcgeoghan wrote:

>The Tests of Within-Subjects effects Greenhouse-Geisser is significant
>.040 and Huynh-Feldt is significant .027 for the MOVES*IAC interaction.
>
>The Tests of Within Subjects Contrasts indicates a significant cubic
>effect (.039) for MOVES*IAC.

That *may* mean what it says it means, but I recommend caution  in
interpreting higher-order polynomial effects, unless you have a lot of
data with good resolution.

On a quick glance through your postings, I don't see your sample size;
but for this, it should be *BIG*. (How many degrees of freedom in your
model? I'm being sloppy here, but isn't it about 30?)

If I understand what you're seeing, it's that, having found the
best-fitting polynomial with the 10-level interval variable MOVES
within each of the three levels of IAC, the cubic terms of these
polynomials differ significantly between levels.

It takes a lot of discriminatory power to even 'see' a cubic term.
Think like this:

. The linear term is what we all know and love: an effect that plots Y
vs. X as (surprise) a straight line.

. The quadratic term may measure a U-shaped effect: Y is high at the
extreme values of X, low at the intermediate values. (Look for this if
the linear term is small.) Or, it may mean an accelerating or
decelerating effect: the effect of the same change in X is considerably
larger at one end of the scale, than at the other. (This will usually
go with a significant linear term.)

. The cubic term is acceleration or deceleration at the scale
*extremes*: the effect of changes of X on Y is higher (or lower) near
both extremes of the scale, than near the middle.

(All this assumes that if any polynomial term is in the model, all
lower terms are as well. That is standard practice, and strongly
recommended.)

If I saw what you're seeing, I'd inspect very carefully: for each level
of IAC, plot your independent (MOVES) vs. the polynomial in variable
'trial' (WS factor, move number 1-10). Since it looks like you have an
ANOVA-like problem, i.e. multiple observations per cell, you'd want the
mean value of MOVE with a standard-deviation error bar, at each point.

I'd watch, specifically, for very large values ('outliers') in data for
the higher or lower move numbers. Following current statistical wisdom,
'outliers' are not to be rejected out of hand. But they're to be
inspected carefully, lest they be simply wrong - blunders in
measurement or data entry.

Real 'outlier' values are, well, real, and must be accounted for in
analysis. But there's always question whether they're a atypical from
the influence of some important unobserved effect.

At best, a small fraction of vary large values raises Cain with the
estimation robustness of any linear model.

-Cheers, and good luck,
  Richard

[statisticsdoc]

Paul,

I would second Richard's suggestions about checking for outliers and looking
at the trends in the actual data.  The cubic trend is sometimes hard to
visualize.  You are looking for a trend that looks like a stretched out S -
something with two inversion points (two places where the line changes
direction), rather than the single inversion point you see in a quadratic
trend (like a U shaped function).  One common type of cubic trend involves a
threshold, where Y is low for low values of X, then Y jumps up for moderate
values of X, then Y remains high for high values of X (or vice versa).  I am
not sure what practical context you are dealing with, but this type of trend
is pretty common in learning experiments.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Paul Mcgeoghan
Sent: Monday, February 05, 2007 8:27 AM
To: [hidden email]
Subject: Re: repeated measures custom contrasts for linear trends


Stephen,

The Tests of Within-Subjects effects Greenhouse-Geisser is significant .040
and Huynh-Feldt is
significant .027 for the MOVES*IAC interaction.

The Tests of Within Subjects Contrasts indicates a significant cubic effect
(.039) for MOVES*IAC.

So yes.

Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).

>>> "Statisticsdoc" <[hidden email]> 05/02/2007 13:17:56 >>>
Paul,

Do you have a significant interaction between MOVES and IAC (i.e., is there
evidence that the slope of the within-subject factor varies as a function of
the between-subject factor)?

Best,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Paul Mcgeoghan
Sent: Monday, February 05, 2007 6:02 AM
To: [hidden email]
Subject: repeated measures custom contrasts for linear trends


Hi,

I have a customer with a within-subject factor (MOVES) with 10 levels and a
between subject factor
with 3 levels (IAC).

He wants to test if there is a linear trend at each of the 3 between subject
factor levels.

What would be the syntax for this?

I currently have the syntax below:

GLM
  moves1 moves2 moves3 moves4 moves5 moves6 moves7 moves8 moves9 moves10 BY
iac
  /WSFACTOR = trial 10 Polynomial
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(iac) COMPARE ADJ(BONFERRONI)
  /EMMEANS = TABLES(trial) COMPARE ADJ(BONFERRONI)
 /EMMEANS = TABLES(iac*trial) COMPARE(iac) ADJ(bonferroni)
 /EMMEANS = TABLES(iac*trial) COMPARE(trial) ADJ(bonferroni)
  /PRINT = DESCRIPTIVE
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = trial
  /DESIGN = iac .

Thanks,
Paul


==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
University Infrastructure Group (UIG),
Information Services,
Cardiff University.
Tel. 02920 (875035).