# calculating a set of z-scores :: Please explain how to represent this procedure

• Aug 1st 2011, 10:23 AM
Vamz
calculating a set of z-scores :: Please explain how to represent this procedure
Hello! I need to know how to represent this procedure mathematically. I am trying to have a program of mine published, but I need to represent this as an equation to the best of my abilities first!

I will first explain how the operation works, and then I will display my attempt at it.

PROCEDURE:
We have two lists of elements: subjects and targets (i's & j's) These elements are actually protein sequences. We have two text files each containing our subjects and targets respectively

Now, we have two functions:
$\displaystyle Sw(i,j) = R$
$\displaystyle Sw^\prime(i) = \{j_1,j_2,j_3\}$

In other words, the Sw() function takes two elements : a subject sequence (i) and a target sequence (j) and returns a raw numerical bit-score called "R".

Now, the Sw'() function will take 1 subject sequence (i) and return 3 targets (j's).

Now, here is the procedure I need proper mathematical syntax: I have I written this in pseudo-code/python (lol)

Code:

from numpy import std,average,shuffle answers = [] shuffled_Rs = [] def myscores(i):   for j in Sw_prime(i):     R = Sw(i,j)     for i in range(500):       shuffled_j = shuffle(j)       shuffled_Rs.append( Sw(i,shuffled_j) )     standard_deviation = std(shuffled_Rs)     average = mean(shuffled_Rs)     z_score = (R - average) / standard_deviation     answers.append(z_score)   return answers
Each R value is normalized by generating 500 more bit scores with shuffled j's, then a standard score is calculated.

Long story short, I feed program one "i" value, and it will return 3 z-scores.
I need to represent this process mathematically. I can define the Sw, Sw' and Shuffle functions in text.

Here is how I attempted it:

Sw’ (i) = {j1, j2, j3} = T
http://i.imgur.com/SPcDP.png

Thanks a lot!