Example 1 - One Factor Design
[Download DOE++ Example File (*.rdoe)]
Background
Consider the following experiment, which was performed at a pulp mill. Plant performance is based on pulp brightness, as measured by a reflectance meter. Each of the four shift operators (denoted by A, B, C and D) made five pulp handsheets from unbleached pulp. Reflectance was read for each of the handsheets using a brightness tester. The data set is shown next.
The goal of the experiment is to determine whether there are differences between the operators in making the handsheets and reading their brightness.
Experiment Design
The experimenters use DOE++ to create a standard one factor design. The design matrix and the response data are given in the "Operator Study" Folio.
Analysis
Step 1: After performing the experiment according to the design and recording the results, the experimenters enter the data set into the Standard Folio, as shown next.
Note that in the figure shown above, the columns have been renamed by double-clicking the column header and entering the new name in the window that appears.
Step 2: The data set is analyzed with the default risk (significance) level of 0.1. Several tables of results are provided on the Analysis tab, which is added to the Folio upon calculation. The first one is the ANOVA table, which is shown next.
The p value is less than the risk level (0.021 < 0.1), indicating that there are significant differences between these four operators.
Step 3: A Box plot is created, as shown next.
The plot shows that operators C and D are almost the same. This is confirmed by the Mean Comparsions table on the Analysis tab, as shown next.
The table also shows that there is no significant difference between operators A and B. The small p values displayed in red indicate significant difference between the compared operators.
Conclusions
From the ANOVA table, the experimenters determine that there is a significant difference between the four operators. The paired comparison shows that the difference between A and B and the difference between C and D are not particularly significant.
