C+-probability

{{DISPLAYTITLE:c⁺-probability}}

In statistics, a c⁺-probability is the probability that a contrast variable obtains a positive value.{{cite journal |author=Zhang XHD

|title= A method for effectively comparing gene effects in multiple conditions in RNAi and expression-profiling research

|journal=Pharmacogenomics |volume=10 |issue= 3|pages=345–58

|year=2009 |pmid=20397965 |doi=10.2217/14622416.10.3.345 }}

Using a replication probability, the c⁺-probability is defined as follows: if we get a random draw from each group (or factor level) and calculate the sampled value of the contrast variable based on the random draws, then the c⁺-probability is the chance that the sampled values of the contrast variable are greater than 0 when the random drawing process is repeated infinite times. The c⁺-probability is a probabilistic index accounting for distributions of compared groups (or factor levels).{{cite book

|author= Zhang XHD

|year=2011

|title= Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research

|publisher =Cambridge University Press

|isbn=978-0-521-73444-8}}

The c⁺-probability and SMCV are two characteristics of a contrast variable. There is a link between SMCV and c⁺-probability.

The SMCV and c⁺-probability provides a consistent interpretation to the strength of comparisons in contrast analysis. When only two groups are involved in a comparison, the c⁺-probability becomes d⁺-probability which is the probability that the difference of values from two groups is positive.{{cite journal |author=Zhang XHD

|title=A new method with flexible and balanced control of false negatives and false positives for hit selection in RNA interference high-throughput screening assays

|journal=Journal of Biomolecular Screening |volume=12 |issue= 5|pages=645–55

|year=2007 |pmid= 17517904|doi=10.1177/1087057107300645 |doi-access=free}} To some extent, the d⁺-probability (especially in the independent situations) is equivalent to the well-established probabilistic index P(X > Y). Historically, the index P(X > Y) has been studied and applied in many areas.{{cite journal |vauthors=Owen DB, Graswell KJ, Hanson DL |title=Nonparametric upper confidence bounds for Pr(Y < X) and confidence limits for Pr(Y < X) when X and Y are normal |journal=Journal of the American Statistical Association |volume=59 |pages=906–24

|year=1964 |doi= 10.2307/2283110|hdl=2027/mdp.39015094992651|hdl-access=free}}

{{cite journal |vauthors=Church JD, Harris B |title=The estimation of reliability from stress-strength relationships

|journal=Technometrics |volume=12 |pages=49–54

|year=1970 |doi= 10.1080/00401706.1970.10488633}}

{{cite journal |author=Downton F

|title=The estimation of Pr(Y < X) in normal case

|journal=Technometrics |volume=15 |pages=551–8

|year=1973 |doi= 10.2307/1266860}}

{{cite journal |vauthors=Reiser B, Guttman I |title=Statistical inference for of Pr(Y ≤ X) – normal case

|journal=Technometrics |volume=28 |pages=253–7

|year=1986 |doi= 10.2307/1269081}}

{{cite journal |vauthors=Acion L, Peterson JJ, Temple S, Arndt S |title=Probabilistic index: an intuitive non-parametric approach to measuring the size of treatment effects

|journal=Statistics in Medicine |volume=25 |issue= 4|pages=591–602

|year=2006 |pmid= 16143965|doi= 10.1002/sim.2256 }} The c⁺-probability and d⁺-probability have been used for data analysis in high-throughput experiments and biopharmaceutical research.