Probit

The probit function converts a probability, a number between 0 and 1, into a score expressing how many standard deviations that value lies from the mean of a standard normal distribution; a probability of 0.5 corresponds to a probit of 0, while a probability of 0.025 corresponds to a probit of about negative 1.96. Formally, the probit is the quantile function, the inverse of the cumulative distribution function, of the standard normal distribution. It originated in toxicology, where it was used to analyze dose-response relationships such as how the effectiveness of a pesticide changes with dose, and it remains central to probit models, a form of regression analysis for binary outcomes, as well as to the construction of Q-Q plots used to check whether a data set follows a normal distribution.