# How to combine unbound variables with very different frequency distributions?

I want to combine three unbound variables. Each variable is the score provided by three different algorithms. Each algorithm predicts the likelihood (score) that a specific interaction between two molecules takes place. I have a gold standard with which I can rate the performance of each algorithm (that is, how many predicted interactions actually take place in real life).

My goal is to come up with a combined score for each interaction, using the scores from the individual algorithms. Ex: interaction1 is predicted by algorithm1: $756$ score, algorithm2: $0.7$, algorithm3: $6.5$

Each has different samples sizes and frequency distributions. Example:

score1: from 1000 to 0, huge peak around 895
score2: from 1 to .5, looks like a standard distribution
score3: from 10 to 0, huge peak around .1
...

My first idea was to normalize each score using $\frac{X-min(X)}{max(X)-min(X)}$, and then do a weighted average with each score: $combinedScore=weight1*score1 + weight2*score2 + weight3*score3$. I get the weights from another variable.

Should I use z-scores, or the logistic function to normalize? Am I doing something wrong?

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Why do you want to normalize the data points first? May be you just want to find a linear combination that explains most of the variation in 3 variable triplets? Simply if you do normalization then it seems to give you back symmetrically-like distributed score and? do you need this one? –  Dmitrij Celov Aug 3 '11 at 12:52
Clarification on the point of combining them would likely be helpful. Dmitrij mentions one possibility, (explaining the most variation). –  Andy W Aug 3 '11 at 12:56
When you say "each has different sample sizes" - can you clarify? Not to be pedantic, I don't think you mean what I mean. :) –  Iterator Aug 3 '11 at 22:21
@Iterator I might have used the wrong terminology. I mean that each variable has a different number of values (score1 has 10K datapoints, score2 5500, score3 7500, for example) –  nachocab Aug 3 '11 at 22:59
@nachocab Can you give an example of your data? I'm not clear what your observations are like. –  Iterator Aug 3 '11 at 23:02