Dummy coding and testing a hypothesis with linear contrasts

Question

I am thinking about this for some time now and can't figure out what I am doing wrong. So I want to compare the performance of doctors (measured in the number of detected vessels) among different automated visual aids. Their task is to detect vessels in an x-ray scan. They are assisted by some software to color the vessels.

I have An old automatic algorithm

A new one

And one that requires some manual guidance

I also want to measure their performance across different degrees of "strength of contrast in the x-ray scan" I dummy coded the three algorithms with "manual guidance" as the reference group (0).

I want to test three hypothesis

A) "automation new" is better than "automation old" one

B)" automation news" performance decreases less over decreases of "strength of contrast" than "automation old" does

C) both automations are worse than the manual one

So I end up with an equation that includes two categorical regressors(Dold,Dnew), a metric one(strength of contrast "b"), and two interaction terms of the performance of the automations across different degrees of strength of contrasts(Doldx and Dnewx)

Y=a+bx+Dold+Dnew+Doldx+Dnewx

The linear contrasts for (A) would be

0

For b

0>a0+ b0+Dold0+Dnew0+Dold1+Dnew-1 0>0,0,0,0,1,-1

But how do I test (c)?

This would violate the constrain that the contrast has to sum to 0

0=a0+b0+Dold1/2+Dnew1/2+Doldx+Dnewx

Can anyone help me out?

Answer 1

Regression means that the right hand statement (RHS) predicts the left hand statement (LHS). You can set up three different models and compare the adjusted R2 for each model. This can be achieved using stepwise regression.

For A) dummy coding is sufficient. You can constrain the regression model by ignoring the third data column, but it would be wise to test that too.

Performance = Intercept + New

For B), If you wish to compare slopes, you should consider if linear models will provide a sensible answer.

Change in Performance = Intercept + NewChange

For C), you compute a new dummy that is 1 for manual and 0 for both automation columns:

Model Validity = Intercept + Manual