# Mathematical notation for formulating a rank score

This is a cross-post from Mathematics forum. As no one has answered it yet, I fIgured post here as well.

I would like to describe a transform I used to rank my data points. I have recoded my variable columns from $10$ measurements with different range to $n$ (for each measurement) where $n \in \{0,0.5,1\}$.

For columns where measurements were expressed as categorical values I simply recoded the categorical value to either $0$, $0.5$ or $1$ and for continuous variables I recoded the lower quartile as $0$, interquartile as $0.5$ and upper quartile as $1$ and finally I summed the recoded values to produce a single score $\sum n_{i1,..i10}$ for each row.

I am trying to write my method and I'd like to have it in mathematical notation. I was wondering if anyone could help me with this!

• Maybe try stats.stackexchange.com Aug 2, 2017 at 22:09
• What do you mean by "have it in mathematical notation"? Can you give an example of something you consider "in mathematical notation"?
– bli
Aug 3, 2017 at 7:54
• Also, it would be good to include the link to the cross-post
– bli
Aug 3, 2017 at 7:55
• Hi bli, Thank you for your comment. By mathematical notation I mean mathematical representation of my transform. I am including the link as you suggested!
– RJF
Aug 3, 2017 at 9:29
• Your question is not very clear to me. So can you please try to explain it with some example. Then we may able to help you. Aug 4, 2017 at 9:45

Here is my solution to the problem. I am posting it here in case anyone else come up with the same idea but did not know how to formulate it in mathematical notation!

$$\psi_i = \sum_{i=1}^9 S_i$$

where $S_i$ is the score function and defined as:

$$S_i = \cases{ 0 & \text{if \theta(x_i) < Q_1 or \theta(x_i) =  benign/neutral} \\ 0.5 & \text{if Q_1 \leq \theta(x_i) < Q_3 or \theta(x_i) =  possibly damaging/uncertain} \\ 1 & \text{if \theta(x_i) \geq Q_3 or \theta(x_i) =  damaging} }$$

The $\theta(x_i)$ is the pathogenicity or conservation score for variant $x$ as defined by model $i$ and $Q$ denotes the quartile range for scores from M-CAP, CADD, GERP and Phylop models.

• If Q are quartiles, then the last line for damaging shouldn't be $>Q_3$?
– llrs
Aug 18, 2017 at 9:47
• @Konrad and Reza : Can you look into this problem and provide some suggestions. math.stackexchange.com/questions/2716192/… Mar 31, 2018 at 15:59