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I have multiple vectors of letters, in which an entry can appear multiple times. The vectors are of variable length. 

ACBDEABAEE
ACDE
ACBDBBDDE

I want to determine statistically if A or C occurs mostly at the beginning of the list, whereas E occurs towards the end and D occurs in the middle.

Is there a way to do this?

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  • $\begingroup$ Against what null hypothesis? That - conditionally on the number of each value, they're just randomly placed - or something else? $\endgroup$
    – Glen_b
    Commented Mar 18, 2014 at 19:26

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Several methods occur to me:

1) Define what you mean by "toward the beginning", "middle" and "toward the end", then do a chi-square analysis:

           B       M     E
A
B
C
D
E

This only tells you if the order is associated with the letter, but you can see from the results which comes first most.

2) For each letter in each list, compute a measure of place in the list. The most obvious is proportion of the list that comes before the letter. Then use that as a dependent variable and letter as an independent variable.

3) If you are just interested in which comes before which, compute a set of duples or triples and see which are most frequent.

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  • $\begingroup$ One way would be to find the average proportion of letters that come after your letter; e.g. ABABC - 4/5 come after first A and 2/5 come after 2nd A, average is 3/5. Then that could be the DV in a logistic regression. $\endgroup$
    – Peter Flom
    Commented Mar 18, 2014 at 19:56

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