# c^{+}-probability

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

- Contrast (statistics)
- Effect size
- SSMD
- SMCV
- Contrast variable
- ANOVA

## References

- ↑
^{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. - ↑
^{2.0}^{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. - ↑ 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 |