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What is the term for the influence of a test on its results?

I think the term you are looking for is “bias”?

I this that Bias is the influance it self I am looking for a term that is descriping a unique influance where preforming the test itself will change the results.

Instrument reactivity?

Maybe you’re thinking of ** self fullfilling prediction** and self-defaeting prediction

Self fullfilling - an economist predicts ecomomic collapse, the prediction causes panic, panic causes collapse. If he hadn’t made the prediction, the collapse might not have happened.

Self defeating - an economist predicts economic collapse. Because they have the information, the Govt act to stop it. The collapse never happens. If he hadn’t made the prediction, the collapse would have happened. But because he did, it didn’t.
Is that what you meant?

Heisenberg uncertainty principle: the results of an observation are affected by the fact it is being observed. This is a term from physics, but the same thing applies to any observation.

No, sorry. This is not quite correct. From (among other sources) a Wikipedia article: