The method that Minitab uses to draw the half normal effects plot depends on the degrees of freedom for the error term.
If the error term has one or more degrees of freedom, Minitab plots the normal scores, probabilities or percentages versus the standardized effects. The line corresponds to a normal distribution with a standard deviation of 1. Effects with p-values less than α are labeled significant on the graph. Minitab labels this graph Half Normal Plot of the Standardized Effects.
If the error term has zero degrees of freedom, Minitab plots the normal scores, probabilities or percentages versus the nonstandardized effects. The line corresponds to a normal distribution with a standard deviation given by Lenth's pseudo standard error. Effects with an absolute value exceeding the margin of error (ME) are labeled significant on the plot. Margin of error is:
where t is the (1 – α / 2) quantile of a t-distribution with degrees of freedom equal to the (number of effects / 3).
The half normal effects plot uses half normal plot points, which are based on the distribution of the absolute value of a standard normal random variable. The cumulative distribution function associated with the half normal plot is:
where Φ is the cumulative distribution function for the standard normal distribution.
For more information on how Minitab calculates PSE, go to the section on Lenth's pseudo standard error.