In statistics, a c+-probability is the probability that a contrast variable obtains a positive value. 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).
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. 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.     The c+-probability and d+-probability have been used for data analysis in high-throughput experiments and biopharmaceutical research. 
- Zhang XHD (2009). "A method for effectively comparing gene effects in multiple conditions in RNAi and expression-profiling research". Pharmacogenomics 10 (3): 345–58. doi:10.2217/146224184.108.40.2065. PMID 20397965.
- Zhang XHD (2011). Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research. Cambridge University Press. ISBN 978-0-521-73444-8.
- Zhang XHD (2007). "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 of Biomolecular Screening 12 (5): 645–55. doi:10.1177/1087057107300645. PMID 17517904.
- "Nonparametric upper confidence bounds for Pr(Y < X) and confidence limits for Pr(Y < X) when X and Y are normal". Journal of the American Statistical Association 59: 906–24. 1964. doi:10.2307/2283110.
- "The estimation of reliability from stress-strength relationships". Technometrics 12: 49–54. 1970. doi:10.1080/00401706.1970.10488633.
- Downton F (1973). "The estimation of Pr(Y < X) in normal case". Technometrics 15: 551–8. doi:10.2307/1266860.
- "Statistical inference for of Pr(Y ≤ X) – normal case". Technometrics 28: 253–7. 1986. doi:10.2307/1269081.
- "Probabilistic index: an intuitive non-parametric approach to measuring the size of treatment effects". Statistics in Medicine 25 (4): 591–602. 2006. doi:10.1002/sim.2256. PMID 16143965.
Original source: https://en.wikipedia.org/wiki/ C+-probability. Read more