# Key results for Tolerance Intervals (Nonnormal Distribution)

Complete the following steps to interpret tolerance intervals.

## Step 1: Assess the distribution fit of the data

Minitab provides tolerance intervals for a method that uses a distribution and a nonparametric method. If you can safely assume that your data follow the distribution, then you can use the tolerance interval for the method that uses the distribution. If you cannot safely assume that your data follow the distribution, then you must try a different distribution or the tolerance interval for the nonparametric method.

To determine whether you can assume that the data follow the distribution, compare the p-value from the Anderson-Darling test to the significance level (α). A significance level of 0.05 indicates a 5% risk of concluding that the data do not follow the distribution when the data do follow the distribution.

P-value ≤ α: The data do not follow the distribution (Reject H0)
If the p-value is less than or equal to the significance level, you can conclude that your data do not follow the distribution. In this case, you must try a different distribution or the tolerance interval for the nonparametric method.
P-value > α: You do not have enough evidence to conclude that the data do not follow the distribution (Fail to reject H0)
If the p-value is larger than the significance level, you do not have enough evidence to conclude that the data do not follow the distribution. In this case, you can use the tolerance interval for the method that uses the distribution.

## Step 2: Examine the tolerance interval from the appropriate method

Minitab provides tolerance intervals for the method that uses the distribution and the nonparametric method that does not assume a particular distribution. You can create a two-sided tolerance interval, or a one-sided tolerance interval that provides an upper bound or a lower bound.
Two-sided
Use a two-sided interval to determine an interval that contains a certain minimum percentage of the population measurements.
Upper bound
Use an upper bound to determine a limit that exceeds a certain minimum percentage of population measurements.
Lower bound
Use a lower bound to determine a limit that is less than a certain minimum percentage of population measurements.
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