CODEWITHSUNDEEP
mathnormalize
Rutger Hofste
Rutger Hofste

Reputation: 4373

convert/normalize raw values on a continuous scale [0-inf] to another continuous scale (score) with range [0-5]

The goal is to convert/normalize raw values on a continuous scale [0-inf] to another continuous scale (score) with range [0-5].

I am using an older study that uses the following approach that I try to reverse engineer:

enter image description here

the equation to convert a raw_value into a score is:
=MAX(0,MIN(5,(LN(raw_value)-LN(0.1))/LN(2) +1))

which means that values are logarithmic interpolated.

enter image description here So a value of 0.125 corresponds to 1.32 and a value of 0.95 corresponds to 4.25 etc.

The objective is to update the thresholds [0.1,0.2,0.4,0.8]

to new thresholds: [0.05,0.25,0.5,0.75]

in other words, values between 0.25 and 0.5 should correspond to scores between 2.x and 3.x.

It looks so simple but I am stuck at something like: =MAX(0,MIN(5,(LN(raw_value)-LN(0.05))/LN(?) +1))

is it even possible to come up with a single equation (No If statements) for the new thresholds since they are a non-logarithmic sequence?

Upvotes: 0

Views: 276

Answers (1)

goutnet
goutnet

Reputation: 442

Well, your problem is that actually your scale is clamping at its border, so it is in fact not linear.

limit to infinity

and

limit to 0+

Using this formula, you are not doing a bijection from R+ to 0 to 5 ... and thus you need your min/max clamping.

Also, please note that your equation is not defined for r=0 ...

You could do something about the lower bound, by using r+1 instead of r in your log, this way, for r=0, ln(r+1)=ln(1)=0

now for the higher bound, unfortunately, using a simple ln scale, you will still aim at limit to 0+. To deal with this, you will need to clamp your input range, and normalize the input by the range.

Upvotes: 1

Related Questions