For each contrast, a tratio is computed by dividing the contrast by the PSE. The reference distribution of these tratios under the null hypothesis is not computationally tractable. Therefore, it is obtained by simulation. The method, described below, is based on a discussion in Ye and Hamada (2000).
Of primary importance in screening experiments is the individual error rate, namely the probability of declaring a given effect as active when it is not. For the ith effect, this occurs when ti is large and falls into the upper tail of its reference distribution.
Because the platform constructs a relatively large number of effects, the experimentwise error rate is also of importance. The experimentwise error rate is the probability of declaring any effect as active when no effects are active. An experimentwise error occurs when no effects are active and the maximum of the absolute tratios, maxti, is large and falls into the upper tail of its reference distribution.
The Fit Two Level Screening platform obtains reference distributions for both types of error rates using Monte Carlo simulation. Consider a set of n  1 values that is simulated from a normal distribution with mean 0 and standard deviation equal to PSE. This set of values represents potential contrast values for the experiment under the null hypothesis of no active effects. In all, 10,000 sets of n  1 random contrast values are generated.
Consider the ith contrast. Lenth tratios are constructed using each of the 10,000*(n  1) simulated values. The reference distribution for the individual error rate is approximated by the absolute values of these tratios. The Individual pvalue is the interpolated fractional position of the observed absolute Lenth tRatio among the 10,000*(n  1) simulated absolute tratios arranged in descending order. This approximates the area to the right of the absolute value of the observed absolute Lenth tRatio with respect to the reference distribution.
An experimentwise error occurs if any tratio leads to rejecting the null hypothesis when all effects are inactive. Equivalently, an experimentwise error occurs if the maximum of the absolute tratios, maxti, leads to rejecting the null hypothesis.
To obtain a reference distribution in this case, consider the maximum of the computed absolute tratios in each of the 10,000 simulations. These 10,000 maximum values form the reference distribution. The Simultaneous pvalue is the interpolated fractional position of the observed absolute Lenth tRatio among the 10,000 simulated maximum absolute tratios arranged in descending order. This approximates the area to the right of the absolute value of the absolute Lenth tRatio with respect to the reference distribution based on the simulated maximum absolute tratios.
To change the number of default sets of simulations from 10,000, you must assign a value to a global JSL variable named LenthSimN. The number of simulations used to derive the pvalues is reported in the report window.
1.

2.

Select Analyze > Specialized Modeling > Specialized DOE Models > Fit Two Level Screening.

3.

4.

5.

Click the red triangle next to Screening for Percent Reacted and select Save Script > To Script Window.

6.

Insert LenthSimN=50000; as the first line of the script.

LenthSimN=50000;
Fit Two Level Screening(
Y( :Percent Reacted),
X( :Feed Rate, :Catalyst, :Stir Rate, :Temperature, :Concentration )
);
7.

Rightclick in the script window and select Run Script.

Note: If LenthSimN=0, the standard tdistribution is used and simultaneous pvalues are not provided. This approach is not recommended.