Notation in Probability and Statistics - Critical Values

Critical Values

The α-level upper critical value of a probability distribution is the value exceeded with probability α, that is, the value x_α such that F(x_α) = 1 − α where F is the cumulative distribution function. There are standard notations for the upper critical values of some commonly used distributions in statistics:

• z_α or z(α) for the Standard normal distribution
• t_α,ν or t(α,ν) for the t-distribution with ν degrees of freedom
• or for the chi-squared distribution with ν degrees of freedom
• or F(α,ν₁,ν₂) for the F-distribution with ν₁ and ν₂ degrees of freedom