# Analysing choices pattern

we have a process in which, at each step, a set of elements are presented to user, the user choses one, his choice is recorded and next round starts with a new set of elements.
For example:
1. {20,50,80} and the user chose 80
2. {80,110,140} and the user chose 80 again
3. ...

We want to verify the hypothesis whether the user prefers large elements. You can assume we have many steps.

How does the following suggestion fare ?

• at each step compute MEAN, and STD of the presented values.
• normalize elements and the choice to be in standard units, i.e.

 standard_value = (value-MEAN) / STD


for example: in (1) above the used chose -1 and in (2) he chose +1

• count how many times each standard unit is chosen and draw a scatter plot.

So for example we'll plot points like: (-3.5,0), (-1.3, 2), (0,4), (1,7), (2,10),

Is this too simplistic ?

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What i would do is i would convert the choices in ranks: {20,50,80}->{1,2,3},{80,110,140}->{1,2,3}, then apply a frequency test to that. –  user603 Jun 27 '12 at 11:15
This will not be good, because ranking strips the relative size information from the set of presented elements. for example: "{1,2,3,100000} -> 3 is chosen" is a strong evidence against the hypothesis while "{1,2,3,4} -> 3 is chosen" is not as strong. –  Sabih Agbaria Jun 28 '12 at 13:42
ok, i had misunderstood, the hypothesis: i thought you wanted to test whether the largest of the proposed set (of three) always ends up being chosen. Thanks for the clarification. –  user603 Jun 28 '12 at 15:10