The Problem
Mike Jay gets different results with different measures
This should not be a surprise that the same people attain different scores and item orderings based on which instruments were used to measure stage
This poster will present a set of reasons
People Do Not Have to Score at the Same Stage Of Performances Across Tasks
There is only one sequence of orders of hierarchical orders of complexity
All sequences have the same orders of complexity no matter what the domain and content
But orders of hierarchical complexity are ordinal
They are not linear
So performance on task A does not have to be comparable to performance on task B. 
Performance on Order A task could be = to that of Order B task
Performance on Order A task could be lower than on Order B task
Performance on Order A could be non comparable to the Order B
Therefore, there is no necessity for the stage of performances across tasks to occur at the same time
If they were linear and the three types of variable discussed below did not make such large differences, they would line up
Sentential Order 5 Actions: Defined In Terms Of Nominal Order 4 Actions & Non-arbitrarily Organize Them

The Three Main Types Of Properties That Affect Stage Of Performance
Stimulus properties
Performance properties
Support properties

Stage developmental measures and instruments are based upon a mixture of
Developmental theories
Measurement methods
Metrics
Contents
Contexts
All these variables produce differences

Many instruments have mixed content and measurement items
Many instruments have not been subjected to even the minimal psychometric tests
Such tests would allow for eliminating items that do not work
Many instruments do not have a clear theory that can be applied to test whether the items meets the criterion of that theory
What Do Various Instruments Really Measure?  Their Stimulus Properties
Scoring or testing something for stage depends on discerning the structure of items or answers
In addition, one needs
Context
Content
Items cannot be written without a context and content
Answers cannot occur to questions without a content and context

The content and context of a task are domain specific
Content and context might be quite idiosyncratic
How idiosyncratic might depend on
How familiar participants are with the content and its use
How much the task and scoring are based on hierarchical complexity of the task
What Do Various Instruments Really Measure?  Their Performance Properties
There are many dimensions to performance
Size of vocabulary
Length of responses
Stage of responses
Range of participant stage
Instruments that do not control for even one of these do not have clear meanings

Performances consist of many variables
Items have many characteristics beyond hierarchical complexity
These include
Number of actions required
Placement of the information
How many stimuli have to be viewed
How long the stimulus items are

What Do Various Instruments Really Measure?  Their Level of Support
Measured stage also is determined by level of support as Arlin (1975) and Fischer et al (1984) have shown
In problem finding, one level of support is taken away
Inhelder and Piaget (1958) used no level of support
Fischer uses one level of support by demonstrating tasks and solutions

Each positive level of support makes the top possible performance one stage higher
Each negative level of support makes the top possible performance one stage lower
Measuring people inventing new solutions in business would provide one level of negative support
Training them to do a job would provide them one positive level of support

Discussion
Regressions of Rasch Scores on the Order of Hierarchical Complexity of items show how much a task is truly a stage task
This is shown by how well the Order of Complexity of a task item predicts performance
Factor Analysis and Rasch Analysis might be used to see how stage-based a scoring scheme is