Converting NCE Score to Weighted Average or to an older NCE score

Recall that scores are calculated as follows:

Raw Score=weighted average -> Converted to a Z score (using mean M and std STD) -> Transformed to an NCE Score (mean 50, std 21.06)

So, to convert a raw score to an NCE score you need a mean (M) and standard deviation (STD).

Sometimes we change the mean and std for a specific test based on test results for that test.

Before we have enough test results, we use the standard values which are:

M=54.29
STD=10.59

These scores were based on the first ~1,000 job specific tests completed on our system (computed across all job specific tests).

However, most tests now use a different M and STD based on results of that specific test.

Sometimes a client wants to go back.

To go back, you must convert from NCE back to Z and then back to raw using the old M and STD and then go forward using the new M and STD.

The values:

S1 = New Overall NCE Score we have now.  (uses M1 and STD1)
S2 = New Overall NCE Score we want to calculate. (uses M2 and STD2)
Z1 = old Z score
Z2 = new Z score

The Calculation - to get S2 from S1

So, give a score S1 created with mean M1 and std STD1, if we want to convert to a score with M2 and STD2 we do this:

Z1 =(S1 - 50)/21.06

Raw = Z1*STD1 + M1

Z2=(Raw - M2)/STD2

S2 = Z2*21.06 + 50