formulasearchengine - User contributions [en]

NADH kinase

2014-04-09T13:27:38Z

85.211.102.160:

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Doctor sweetening process

2013-08-31T03:05:34Z

85.211.96.68:

{{Cleanup|date=September 2008}}
{{technical|date=June 2012}}
'''Retention distance''', or ''RD'', is a concept in [[thin layer chromatography]], designed for quantitative measurement of ''equal-spreading'' of the spots on the chromatographic plate and one of the [[Chromatographic response function]]s. It is calculated from the following formula:

<math>
R_D = \Bigg[(n+1)^{(n+1)} \prod^n_{i=0}{(R_{F(i+1)}-R_{Fi})\Bigg]^{\frac{1}{n}}}
</math>

where ''n'' is the number of compounds separated, ''Rf (1...n)'' are the [[Retention factor]] of the compounds sorted in non-descending order, ''Rf0'' = 0 and ''Rf(n+1)'' = 1.

== Theoretical considerations ==

The coefficient lies always in range <0,1> and 0 indicates worst case of separation (all Rf values equal to 0 or 1), value 1 indicates ideal equal-spreading of the spots, for example (0.25,0.5,0.75) for three solutes, or (0.2,0.4,0.6,0.8) for four solutes.

This coefficient was proposed as an alternative to earlier approaches, such as delta-Rf, delta-Rf product or MRF (Multispot Response Function). Besides its stable range, the advantage is a stable distribution as a random variable, regardless of compounds investigated.

In contrast to the similar concept called [[Retention uniformity]], ''Rd'' is sensitive to ''Rf'' values close to 0 or 1, or close to themselves. If two values are not separated, it is equal to 0. For example the ''Rf'' values (0,0.2,0.2,0.3) (two compounds not separated at 0.2 and one at the start ) result in ''RD'' equal to 0, but ''RU'' equal to 0.3609. When some distance from 0 and spots occurs, the value is larger, for example ''Rf'' values (0.1,0.2,0.25,0.3) give ''RD'' = 0.4835, ''RU'' = 0.4066.

== See also ==

* [[Chromatographic response function]]

== References ==

* Komsta Ł., Markowski W., Misztal G., A proposal for new RF equal-spread criteria with stable distribution parameters as a random variable. J. Planar Chromatogr. 2007 (20) 27-37.

[[Category:Chromatography]]

{{analytical-chem-stub}}

Autoxidation

2013-08-31T01:49:13Z

85.211.96.68: /* Autoxidation in food */

{{distinguish|z-score|z-value}}
{{about|the Z-factor in statistics|the gas compressibility factor|Compressibility factor}}

The '''Z-factor''' is a measure of [[statistics|statistical]] [[effect size]]. It has been proposed for use in [[high-throughput screening]] (where it is also known as Z-prime,<ref>http://planetorbitrap.com/data/uploads/4fb692e73c07b.pdf</ref> and commonly written as Z') to judge whether the response in a particular [[assay]] is large enough to warrant further attention.

==Background==
In high-throughput screens, experimenters often compare a large number (hundreds of thousands to tens of millions) of single measurements of unknown samples to positive and negative [[scientific control|control]] samples. The particular choice of experimental conditions and measurements is called an assay. Large screens are expensive in time and resources. Therefore, prior to starting a large screen, smaller test (or pilot) screens are used to assess the quality of an assay, in an attempt to predict if it would be useful in a high-throughput setting. The Z-factor is an attempt to quantify the suitability of a particular assay for use in a full-scale, high-throughput screen.

==Definition==
The Z-factor is defined in terms of four parameters: the [[expected value|mean]]s and [[standard deviation]]s of both the positive (p) and negative (n) controls (<math>\mu_p</math>, <math>\sigma_p</math>, and <math>\mu_n</math>, <math>\sigma_n</math>). Given these values, the Z-factor is defined as:

:<math>\text{Z-factor} = 1 - {3 (\sigma_p + \sigma_n) \over | \mu_p - \mu_n |}.</math>

In practice, the Z-factor is estimated from the [[arithmetic mean|sample mean]]s and sample standard deviations

:<math>\text{Estimated Z-factor} = 1 - {3 (\hat{\sigma}_p + \hat{\sigma}_n) \over | \hat{\mu}_p - \hat{\mu}_n |}.</math>

==Interpretation==
The following interpretations for the Z-factor are taken from:<ref name=ZhangJHetal1999>{{cite journal |author=Zhang JH, Chung TDY, Oldenburg KR
|title=A simple statistical parameter for use in evaluation and validation of high throughput screening assays
|journal=Journal of Biomolecular Screening |volume=4 |issue= |pages=67–73
|year=1999 |month= |pmid=10838414 |doi=10.1177/108705719900400206 |url=}}</ref>

{| class="wikitable"
! Z-factor !! Interpretation
|-
|1.0||Ideal. Z-factors can never exceed 1.
|-
|between 0.5 and 1.0||An excellent assay. Note that if <math>\sigma_p = \sigma_n</math>, 0.5 is equivalent to a separation of '''12''' standard deviations between <math>\mu_p</math> and <math>\mu_n</math>.
|-
|between 0 and 0.5||A marginal assay.
|-
|less than 0||There is too much overlap between the positive and negative controls for the assay to be useful.
|}

Note that by the standards of many types of experiments, a zero Z-factor would suggest a large effect size, rather than a borderline useless result as suggested above. For example, if σp=σn=1, then μp=6 and μn=0 gives a zero Z-factor. But for normally-distributed data with these parameters, the probability that the positive control value would be less than the negative control value is less than 1 in 105. Extreme conservatism is used in high throughput screening due to the large number of tests performed.

==Limitations==
The constant factor 3 in the definition of the Z-factor is motivated by the [[normal distribution]], for which more than 99% of values occur within 3 standard deviations of the mean. If the data follow a strongly non-normal distribution, the reference points (e.g. the meaning of a negative value) may be misleading. Another issue is that the usual estimates of the mean and standard deviation are not [[robust statistics|robust]]; accordingly many users in the high-throughput screening community prefer "Robust Z-prime".<ref>{{cite journal |author=Birmingham, Amanda, et. al.
|title= Statistical Methods for Analysis of High-Throughput RNA Interference Screens
|journal=Nat Methods |volume=6 |issue=8 |pages=569–575
|date=August 2009 |doi= 10.1038/nmeth.1351 |pmc=2789971}}</ref> Extreme values (outliers) in either the positive or negative controls can adversely affect the Z-factor, potentially leading to an apparently unfavorable Z-factor even when the assay would perform well in actual screening
.<ref name=Sui2007>{{cite journal |author=Sui Y, Wu Z
|title= Alternative Statistical Parameter for High-Throughput Screening Assay Quality Assessment
|journal=Journal of Biomolecular Screening |volume=12 |issue= |pages=229–34
|year=2007 |month= |pmid=17218666 |doi= 10.1177/1087057106296498 |url=}}</ref>
In addition, the application of the single Z-factor-based criterion to two or more positive controls with different strengths in the same assay will lead to misleading results
.<ref name=ZhangetalJBS2008>{{cite journal |author=Zhang XHD, Espeseth AS, Johnson E, Chin J, Gates A, Mitnaul L, Marine SD, Tian J, Stec EM, Kunapuli P, Holder DJ, Heyse JF, Stulovici B, Ferrer M
|title= Integrating experimental and analytic approaches to improve data quality in genome-wide RNAi screens
|journal=Journal of Biomolecular Screening |volume=13 |issue= |pages= 378–89
|year=2008 |month= |pmid=18480473 |doi= 10.1177/1087057108317145 |url=}}</ref> The absolute sign in the Z-factor makes it inconvenient to derive the statistical inference of Z-factor mathematically
<ref name=ZhangGenomics2007>{{cite journal |author=Zhang XHD
|title=A pair of new statistical parameters for quality control in RNA interference high-throughput screening assays
|journal=Genomics |volume=89 |issue= |pages=552–61
|year=2007 |month= |pmid=17276655 |doi=10.1016/j.ygeno.2006.12.014 |url=}}</ref>
. A recently proposed statistical parameter, strictly standardized mean difference ([[SSMD]]), can address these issues <ref name="ZhangetalJBS2008"/>
<ref name=ZhangGenomics2007>{{cite journal |author=Zhang XHD
|title=A pair of new statistical parameters for quality control in RNA interference high-throughput screening assays
|journal=Genomics |volume=89 |issue= |pages=552–61
|year=2007 |month= |pmid= 17276655|doi=10.1016/j.ygeno.2006.12.014 |url=}}</ref>
<ref name=ZhangJBS2008>{{cite journal |author=Zhang XHD
|title= Novel analytic criteria and effective plate designs for quality control in genome-wide RNAi screens
|journal=Journal of Biomolecular Screening |volume=13 |issue= |pages= 363–77
|year=2008 |month= |pmid=18567841|doi= 10.1177/1087057108317062 |url=}}</ref>
. One estimate of [[SSMD]] is robust to outliers.

==See also==
* [[Z-score]] or [[Standard score]]
* [[high-throughput screening]]
* [[SSMD]]

==References==
{{reflist}}

==Further reading==
* Kraybill, B. (2005) [http://iccb.med.harvard.edu/screening/Quantitative%20Assay%20Evaluation%20and%20Optimization%20complete%20(3).pdf "Quantitative Assay Evaluation and Optimization"] (unpublished note)
* Zhang XHD (2011) [http://www.cambridge.org/9780521734448 "Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research, Cambridge University Press"]

{{DEFAULTSORT:Z-Factor}}
[[Category:Change detection]]
[[Category:Effect size]]

Schrödinger equation

2007-03-19T20:26:59Z

85.211.2.242: minor correction - described psi(t) as the "time dependent WF" rather than "WF"

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