Z factor

The Z-factor is a measure of the statistical effect size. It is used for the analysis of high throughput processes in order to decide whether the signal is large enough in a particular experiment to carry out further investigations.

background

In high-throughput processes, several hundred thousand to 10 million individual measurements are often carried out on unknown samples against positive and negative controls . The choice of certain experimental conditions and measurement methods is called "assay". Large-scale analysis is expensive and time consuming. Therefore, pilot experiments on a small scale are carried out in advance in order to assess the informative value of the assay. The Z-factor is a measure for assessing the usefulness of a special assay in high throughput.

definition

The Z-factor is defined by four parameters: the mean and the standard deviation of the positive and negative control. The formula is:

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

Where: σ = standard deviation, µ = mean value, n = negative, p = positive.

In practice, the Z-factor can be approximated with the sample mean and the standard deviation of the sample.

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

interpretation

Z factor	interpretation
1.0	Ideally, z-factors cannot exceed 1.
between 0.5 and 1.0	An excellent assay; note that if , 0.5 is equivalent to a separation of 12 standard deviations between and . ${\ displaystyle \ sigma _ {p} = \ sigma _ {n}}$ ${\ displaystyle \ mu _ {p}}$ ${\ displaystyle \ mu _ {n}}$
between 0 and 0.5	a bad assay
below 0	too much overlap between positive and negative controls

proof

↑ Zhang JH, Chung TDY, Oldenburg KR (1999). A simple statistical parameter for use in evaluation and validation of high throughput screening assays . In: Journal of Biomolecular Screening 4: 67-73. doi : 10.1177 / 108705719900400206 .

literature

Kraybill, B. (2005) "Quantitative Assay Evaluation and Optimization" (unpublished note)
Zhang XHD (2011) "Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research, Cambridge University Press"

[1] Zhang JH, Chung TDY, Oldenburg KR (1999). A simple statistical parameter for use in evaluation and validation of high throughput screening assays . In: Journal of Biomolecular Screening 4: 67-73. doi : 10.1177 / 108705719900400206 .