The probit function.

The probit function is another name for the inverse of the cumulative Gaussian distribution. 

95% of values sampled from a Gaussian distribution lie within 1.96 standard deviations of the mean. Using the variable z to indicate the number of standard deviations above (or below) the mean, this can be restated: 95% of  values in a Gaussian distribution have z between -1.96 and 1.96. This leaves 2.5% of the distribution with z less than 1.96,  and 2.5% of the distribution with z greater than 1.96. 

Another way to say this is that the probit of 2.5% equals -1.96, and the probit of 97.5% is 1.96. 

Prism can compute the probit function as part of its built-in set of transforms.  Notes:

• Prism expects the input to the function to be a fraction, not a percent. Probit(2.5) is not defined. Probit(0.025) is defined.
• While probit() is a built-in transform, that function is not available to use as part of a user-defined transform or equation.
• Prism uses an older definition of probit that adds 5 to all results, to avoid use of negative numbers. No, it doesn't really make sense, but this was once a  common standard. So probit(0.025) = 3.04, which equals -1.96 + 5.00, and probit (.975) = 6.96, which is 1.96 + 5.00. 
• There is a bug in Prism 7 (all releases, Windows and Mac). When the value is greater than 0.5, the probit function is wrong. Rather than calculating Probit(Value), it incorrectly computes Probit(Value - 0.5). Here is an easy workaround. Create a user-defined transform Y= 5.0 - tfromp(Y, 10000). Prism 7 doesn't have an inverse z function, but the inverse t function (tFromP) is the same as the inverse z function when the degrees of freedom are large.
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