What Z′-factor measures
Z′-factor (Z-prime) is a dimensionless score between −∞ and 1 that summarises the separation between your positive and negative controls relative to their combined variability. It was introduced by Zhang et al. (1999) specifically for HTS assay validation.
A Z′ of 1 is a perfect assay, with no variability whatsoever. In practice, anything above 0.5 is considered screening-ready.
| Z′ value | Assay quality | Recommendation |
|---|---|---|
| > 0.6 | Excellent | Proceed to full screen |
| 0.5 – 0.6 | Good | Acceptable; monitor plate by plate |
| 0 – 0.5 | Marginal | Optimise assay before screening |
| < 0 | Failed | Positive and negative controls overlap; do not screen |
The formula
Z′ is calculated from the means and standard deviations of your positive and negative controls on the same plate:
| Variable | Meaning |
|---|---|
| μ₊, μ₋ | Mean of positive and negative controls |
| σ₊, σ₋ | Standard deviation of positive and negative controls |
The numerator captures the combined spread (three standard deviations on each side, a 99.7% confidence envelope). The denominator is the signal window.
Widen either control's spread or pull the means together and watch the 3σ bands eat the signal window, and Z′ collapse:
Z′ = 0.40: marginal: usable but noisy. Z′ rewards a wide gap between controls and punishes their spread: widen either σ or shrink the separation and the 3σ bands eat the signal window. Aim for Z′ ≥ 0.5.
Calculate Z′ per plate, not as a single value across your entire run. A screen with an average Z′ of 0.6 can still contain individual plates with Z′ below 0.3 that would generate unacceptable false-positive rates.
Common causes of low Z′
| Cause | Symptom | Fix |
|---|---|---|
| Small signal window | μ₊ and μ₋ are close together | Optimise compound concentration, cell density, or incubation time |
| High control variability | σ₊ or σ₋ is large | Check dispensing precision; inspect for well-to-well position effects |
| Outlier control wells | One well far from the others | Flag and exclude; investigate pipetting or evaporation |
| Reagent degradation | Decline in Z′ across a multi-day run | Prepare fresh reagent batches; store at correct temperature |
Z′ versus Z-factor
Z′-factor uses only controls. Z-factor (no prime) uses the actual sample distribution versus one control group. For assay validation, always report Z′. Z-factor is occasionally used post-screen to assess hit identification performance.
Never average Z′ across plates to report a single screen-level value. Report the distribution: median, minimum, and the number of plates below threshold. Averaged Z′ conceals plate-level failures.
References
- Zhang, J. H., Chung, T. D. Y., & Oldenburg, K. R. (1999). A simple statistical parameter for use in evaluation and validation of high throughput screening assays. Journal of Biomolecular Screening, 4(2), 67–73.