1. Math Psych 2000 Turning the Process-Dissociation Procedure Inside Out:
A New Approach for Investigating the Relation
Between Controlled and Automatic Influences
Math Psych 2000
Steve Joordens, Daryl Wilson & Thomas Spalek
University of Toronto at Scarborough

2. Be Gentle Stevie Coggies Mathies
Comfort with Mathematical Terms and Concepts

3. SPICE SPI___ SPI___ An Example for Context Study Phase ………….. ……………
Test Phase or
Inclusion Exclusion
Try TO use Try NOT to use
study items study items

4. Performance Assumptions
C&A
C&A C C
C&A
C&A A A
Inclusion = C + A – C&A
Exclusion = A – C&A
Therefore, C = Inclusion - Exclusion

5. Assumptions Concerning the Relation Between Controlled and Automatic Processes
A precise estimate of automatic influences (A) cannot be obtained based on the performance assumptions because there are three unknowns and only two formulae … one of the unknowns needs to somehow become known (or another formula created).
C&A
Assuming independence, C&A = CxA C
C&A
Therefore, A = Exclusion / (1 – C) A

6. Redundancy: An Alternative Assumption
Joordens & Merikle (1993) suggested that one could also assume a redundancy relation between controlled and automatic influences such that controlled influences are assumed to arise from the same processes that gave rise to automatic influences.
C&A
Assuming redundancy, C&A = C C A
Therefore, A = Inclusion
Thus, the estimate of A depends critically on which relation between controlled and automatic influences is assumed

7. Approach/Avoidance How does one proceed from here?
One alternative is to avoid the issue altogether by coming up with other ways of roughly estimating automatic influences … or assessing the interplay between automatic and controlled influences.
In contrast, our view is that the issue of the underlying relation between controlled and automatic influences is critical as it gets at the underlying architecture of cognition. Rather than being a problem for the process-dissociation procedure, it is possible that the process-dissociation procedure may provide a tool for getting at this critical issue. Thus, we vote for approach!

8. Independence vs. Redundancy
Most studies trying to discriminate between the models have really just tried to support or refute the independence assumption. Two versions of this have been promoted …
The Jacoby camp has tried to support the independence assumption by highlighting manipulations that affect estimates of controlled influences, but leave the estimates of automatic influence invariant.
In contrast, Hintzman, Curran and others have refuted the independence assumption by highlighting manipulations that give rise to bizarre effects on the estimates of automatic influences; so called paradoxical dissociations.
Both of these rely on what we would call an outside-in logic …

9. The Outside-In Logic
Begin by doing a study involving some critical manipulation, and obtaining inclusion and exclusion scores under the different levels of that manipulation
Based on the performance assumptions and the independence assumption, compute estimates of C and A
See if the estimates give rise to either invariances or paradoxical dissociations.
We have two major problems with this approach. First, it can only really be used to support or refute independence (and is limited in that respect as well). Second, it requires an assumption of independence to support or refute independence, which is just weird.

10. The Inside-Out Logic
We wish to propose a different (inverted) logic for discriminating between these models – one that begins from the theoretical relations and makes predictions about empirical data. Specifically:
Arbitrarily set values of C and A across wide ranges
Based on these values, and either the independence or the redundancy assumption, calculated predicted estimates of inclusion and exclusion scores
Examine how those estimates should respond to manipulations that affect C or A
See if the real estimates (from the literature) dance in manners more consistent with either the independence or redundancy predictions.

11. For Example
As an illustration of this approach consider the following Monte-Carlo simulation in which we fixed A at 0.5, and allowed C to vary from 0.50 down to 0.00.

12. The Size of A Matters
When the A is high (0.8), the models become similar with respect to their predictions – both predict that exclusion scores will change more than inclusion scores
However, when A is low (0.2), the predictions associated with the two models become divergent because the independence model shifts to predicting a greater change on inclusion than on exclusion scores

13. Generally Speaking Independence Redundancy Inclusion Exclusion
Delta Ratio

14. Evaluation Procedure
We started by looking at 17 studies containing 76 manipulations of controlled influences (instructional manipulations)
Then, we choose only those manipulations in which the absolute value of the change in A was less than 0.1 according to the independence assumption
We then plotted a scatter-plot showing the delta ratio for the empirical data as a function of overall level of A, with the function predicted by the model overlaid on the plot
Then we calculated the mean and standard deviations of the squared residuals, which were compared across models to ascertain which provided the better account of the data

15. Independence
Squared Residuals
Mean = 8.61
SD = 18.69
N = 49

16. Redundancy
Squared Residuals
Mean = 6.58
SD = 14.10
N = 49

17. Comparison of Models
The following comparisons are t-tests comparing the mean squared residuals associated with the two models …
Independence Redundancy t-value
Overall
High A - I
Low A - I
High A – R
Low A – R

18. Conclusions
We see this new “inside-approach” as having several advantages over previous attempts to get at the underlying relation between controlled and automatic influences:
It is far more conducive to a discriminative comparison of the models in question, rather than focusing on one model or the other
It does not require one to assume some underlying model in order to test that model
It truly should have the potential to convincing show one model to be superior to the other in terms of predicting empirical data … thus it should allow stronger conclusions