Comparing real and expected values

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The discussion revolves around a hypothetical experiment testing how participants reach for an object under three different light conditions: dim, bright, and no light. The expected outcome is that participants will predominantly follow trajectory "C" when reaching, defined by a specific arm angle. The conversation seeks advice on the most suitable statistical test to validate this prediction and how to implement it using SPSS software. There is some clarification needed regarding the definition of "expected values" in the context of the experiment. Overall, the focus is on determining the best method to analyze the reaching trajectories in relation to light conditions.
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Hi,

Just a hypothetical problem...

Lets say I test participants in three "light" conditions (dim light,
bright light, no light) to see how they reach an object. There are 20 trials
within each condition.

There are four possible reaching trajectories (A, B, C, and D). Let's define them
by a particular angle of a reaching arm to the frontal plane of a participant.

I expect that performance in any of the
three "light" conditions will follow a trajectory "C", and not any other trajectory.
That is, angles of a reaching arm should correspond to angle of trajectory "C"

What would be the most suitable test of this prediction? How could I conduct such
test in SPSS?

Thanks for your help!
 
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It isn't clear whether you intend "expected values" to have the standard definition used in probability theory. The expected value of a random variable is its mean (or "average") value. It wouldn't necessarily be the value that a person would expect to observe on every realization of the random variable.
 
Hi Stephen,

I will get back to this soon. Thank you.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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