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In statistics, a c+-probability is the probability that a contrast variable obtains a positive value.[1] 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).[2]

The c+-probability and SMCV are two characteristics of a contrast variable. There is a link between SMCV and c+-probability.[1] [2] The SMCV and c+-probability provides a consistent interpretation to the strength of comparisons in contrast analysis.[2] 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.[3] 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.[4] [5] [6] [7] [8] The c+-probability and d+-probability have been used for data analysis in high-throughput experiments and biopharmaceutical research.[1] [2]

See also


  1. 1.0 1.1 1.2 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:10.2217/14622416.10.3.345. PMID 20397965. 
  2. 2.0 2.1 2.2 2.3 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. 
  3. 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. 
  4. "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. 
  5. "The estimation of reliability from stress-strength relationships". Technometrics 12: 49–54. 1970. doi:10.1080/00401706.1970.10488633. 
  6. Downton F (1973). "The estimation of Pr(Y < X) in normal case". Technometrics 15: 551–8. doi:10.2307/1266860. 
  7. "Statistical inference for of Pr(Y ≤ X) – normal case". Technometrics 28: 253–7. 1986. doi:10.2307/1269081. 
  8. "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.