2
$\begingroup$

Given there are two psychological concepts A and B that are considered to be independent/orthogonal.

Would the following empirical results proof the opposite? If not why?

In the first experiment A is the independent variable with two conditions: high and low A. B is identically induced in both conditions and measured as the dependent variable. In the high A condition high B is measured. In the low A condition low B is measured. The second experiment is analog to the first one, except with A and B reversed: in the high B condition high A is measured, and in the low B condition low A is measured.

References to papers that use similiar arguments would be very helpful.

$\endgroup$
2
  • $\begingroup$ This might be more suitable on statistics SE? I see no direct necessary relation to this site. $\endgroup$
    – Steven Jeuris
    Sep 24, 2018 at 11:17
  • $\begingroup$ The questions is about the interpretation of such empirical results in the context of cognitive science research. $\endgroup$
    – thando
    Sep 24, 2018 at 14:20

1 Answer 1

2
$\begingroup$

Since the data show a two-way dependence (low A -> low B, hi A -> hi B and the reverse) this would prove the variables are not independent, as

Linearly independent, orthogonal, and uncorrelated are three terms used to indicate lack of relationship between variables.

Reference
- Rodgers et al., The American Statistician (1984); 38(2): 133-4

$\endgroup$
6
  • $\begingroup$ Thank you for your answer! One follow up question: What can be derived from such a two-way dependence? Might one even say A and B are essentially the same? $\endgroup$
    – thando
    Sep 24, 2018 at 14:17
  • $\begingroup$ @thando My pleasure. They are likely not the same, as no numerical values are given $\endgroup$
    – AliceD
    Sep 24, 2018 at 14:21
  • $\begingroup$ You need to be very careful with the interpretation of non-independence though. Ultimately everything is non-independent (because you can intervene with a brick and send performance on every task to zero, followed by very highly correlated recovery of all abilities). [non]orthogonality is a stronger claim and correspondingly harder to demonstrate. You might want to explore "systems factorial technology" or "Signed difference analysis". $\endgroup$ Sep 24, 2018 at 16:32
  • $\begingroup$ Thank you @steveLangsford, also for the hints! What would be reasonable hypotheses about the relation of the two concepts, given the experimental results in the question above? $\endgroup$
    – thando
    Sep 24, 2018 at 18:48
  • $\begingroup$ From a strict logic perspective the description leaves a pretty wide field of possible relationships still feasible. But presumably there's a lot more constraining information contained in how A and B are supposed to work and the manipulation that was used to fix their levels? $\endgroup$ Sep 24, 2018 at 19:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.