Hi

> We have a problem comparing the strength of regression

> coefficients of the same independent variable in models with

> different dependent variables. Below I will show two

> (related) examples:

> Example 1.

> Cross-sectional design. Dependent variables: two speed tasks

> (number of seconds needed is recorded; the lower, the better,

> the faster) and tasks differ in complexity/difficulty.

> Independent variable: age (0: young and 1: old). Question: do

> older people particularly differ from younger people in the

> difficult task (more so than in the easy task)?

I'm not sure I see the overall difficulty here. Analysis of

variance (or regression equivalent) to analyze the effects of

task, age, and their interaction on RT. If all people performed

both tasks, then task is within-subject factor, otherwise,

between-subjects along with age. In either case, significant

interaction would indicate greater difference between ages for

one of the tasks. Examination of means and perhaps simple

effects of age for 2 tasks would inform the exact conclusion.

One complication is if the two tasks have dramatically different

RTs, in which case you would have to consider whether absolute or

proportional differences were of interest (e.g., significant

interaction could occur for difference of 15 sec vs. 20

sec for easy task, a 33% difference, vs. difference of 30 sec

vs. 40 sec for difficult task, still a 33% difference). Ratio

scores could be calculated if task is within-subjects.

Quote:> Example 2.

> Cross-sectional design. Dependent variables: one speed task

> (number of seconds needed is recorded; the lower, the better,

> the faster) and a memory task (number of words reproduced

> after presentation; the higher, the better (the memory)).

> Independent variable: age (0: young and 1: old). Question: do

> older people particularly differ from younger people in the

> speed task (more so than in the easy task)?

Separate anovas would indicate if significant differences

occurred for speeded task and not for memory task, perhaps the

easiest case to make. If age affected both, there are tests for

the significance of differences between correlation coefficients

(see Quinn McNemar's classic text) that could be used. Since r^2

reflects differences between means relative to total variability

in y, this would seem to parallel the idea of an interaction.

Quote:> Some have suggested MANOVA or GLM repeated measures designs.

> Is this the way to go? And, foremost, should at least the

> dependent variable be standardised then?

Repeated measures would appear to apply to 1st design, assuming

task within-subjects. So, something like

MANOVA easy diff BY age(1 2) /WSF task(2) /PRINT=CELL

/WSD /DESIGN

/WSD task??? MWITHIN task(1) MWITHIN task(2) /DESIGN age

The 1st anova is the default factorial. Look for a significant

interaction. The second is the simple effects of age at each

level of task. (I'm not certain whether to include TASK on the

WSD line for the 2nd design, hence the ???. I find SPSS can do

some weird things when all desired effects are listed for simple

effects).

The interaction above is equivalent to testing significance of

difference between difference scores, that is,

COMPUTE differ = diff - easy

MANOVA differ BY age(1 2) /PRINT = CELL

This equivalence suggests that to address the ratio question, one

could do something like,

COMPUTE ratio = diff/easy

MANOVA ratio BY age(1 2) /PRINT = CELL

For your 2nd situation (speed vs. recall), I would stick with the

difference between rs, because this standardizes the effects.

Best wishes

Jim

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

James M. Clark (204) 786-9757

Department of Psychology (204) 774-4134 Fax

University of Winnipeg 4L05D

CANADA http://www.uwinnipeg.ca/~clark

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