Z-factor

The Z-factor is defined in terms of four parameters: the means (${\displaystyle \mu }$) and standard deviations (${\displaystyle \sigma }$) of samples (s) and controls (c). Given these values (${\displaystyle \mu _{s}}$, ${\displaystyle \sigma _{s}}$, and ${\displaystyle \mu _{c}}$, ${\displaystyle \sigma _{c}}$), the Z-factor is defined as:

${\displaystyle {\text{Z-factor}}=1-{3(\sigma _{s}+\sigma _{c}) \over |\mu _{s}-\mu _{c}|}}$

For assays of agonist/activation type, the control (c) data (${\displaystyle \mu _{c}}$, ${\displaystyle \sigma _{c}}$) in the equation are substituted with the positive control (p) data (${\displaystyle \mu _{p}}$, ${\displaystyle \sigma _{p}}$) which represent maximal activated signal; for assays of antagonist/inhibition type, the control (c) data (${\displaystyle \mu _{c}}$, ${\displaystyle \sigma _{c}}$) in the equation are substituted with the negative control (n) data (${\displaystyle \mu _{n}}$, ${\displaystyle \sigma _{n}}$) which represent minimal signal.

In practice, the Z-factor is estimated from the sample means and sample standard deviations

${\displaystyle {\text{Estimated Z-factor}}=1-{3({\hat {\sigma }}_{s}+{\hat {\sigma }}_{c}) \over |{\hat {\mu }}_{s}-{\hat {\mu }}_{c}|}}$

Z'-factor

The Z'-factor (Z-prime factor) is defined in terms of four parameters: the means (${\displaystyle \mu }$) and standard deviations (${\displaystyle \sigma }$) of both the positive (p) and negative (n) controls (${\displaystyle \mu _{p}}$, ${\displaystyle \sigma _{p}}$, and ${\displaystyle \mu _{n}}$, ${\displaystyle \sigma _{n}}$). Given these values, the Z'-factor is defined as:

${\displaystyle {\text{Z'-factor}}=1-{3(\sigma _{p}+\sigma _{n}) \over |\mu _{p}-\mu _{n}|}}$

The Z'-factor is a characteristic parameter of the assay itself, without intervention of samples.