Relative standing

Relative standing: Where does a score reside compared to everyone else?

Percentiles or ordinal position or rank: is not sensitive to the variability of raw scores, just ranking.

Standard scores (z-scores): Statistical approach to standardizing scores in a standard scale of measurement. The relative standing of one score can be compared to another, even when they are measured on different scales (GMAT, CPA, GRE, etc.). A numerical index of relative standing expressed in standard deviation units. The mean has a z-score of 0 standard deviation units.

Calculated by (score - population mean)/population standard deviation also known as the distance from the mean expressed in standard deviation units.

Formula structure is "observed" minus "expected" divided by "error".

Was Wayne Gretsky a better scorer than Michael Jordan? (Compare z-scores)

If you don't know the population standard deviation, generally you don't calculate z-scores.


Z-distribution (Appendix B, pg B1-B5)

Table calculates the (a) area between the Z score and Mean and (b) area beyond the Z score in a normal distribution.

The "area beyond the Z score" is the probability score.