C+-probability
# C+-probability

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.

