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]}

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