SLAS

# Z' or Z-Score

## Definition

Z' also known as Z-Score is a widely used statistic for assessing data quality of assays with a high and low signal control as often seen in many plate based assays.1

## Formula

Z' = 1 - ((3*SDHi + 3*SDLow)/(AvgHi-AvgLo))

Where,

SDHi =  The standard deviation of the high signal controls.
SDLow = The standard deviation of the low signal controls.
AverageHi = The average of the high signal controls.
AverageLow =  The average of the low signal controls.

## Discussion

Fundamentally Z' is a ratio of the total noise in the control wells divided by the total signal window. Because of this, under the circumstance where noise is extremely limited or the signal window (AvgHi-AvgLo) tends to infinity, the ratio tends to zero causing Z' to approach 1. Defining the lower limit of acceptability is both dependent on lab standards and what is scientifically feasible based on the assay and is the source of much debate. Typical standards allow for a lower acceptable limit of .4 with a desired value of .6-.8 under more robust assay conditions. In general, assays with a Z' > .9 can be considered difficult to attain.