DOE 3² Factorial Using ANOVA

Design of Experiments of two-factors at three levels can be handled using ANOVA.

Case Study

A school wants to increase attendance at business seminars. The administrator has attendance data from two sets of seminars held on Mon/Wed/Fri in 1-2-4 hour lengths:

Which combination of seminar days/times will give the best attendance?

ANOVA Two-Factor with Replication
With the QI Macros, select the data and run ANOVA Two-Factor with (2) replications:

From the p-values, we can see that length, day and interaction affect attendance. If we plot the averages for each length by day we can see that longer Wednesday seminars work best:

Mondays and one-hour seminars simply don't generate the attendance. Two or four hour seminars on Wednesday attract the most attendees. Friday two-hour seminars might also be an option.

What if there were no replications:

ANOVA Two-Factor without Replication would give:

In this case, p-value of 0.053 is slightly larger than alpha=0.05, so we can't confirm that different days and times are statistically significant. A graph of the data does suggest, however, that Wed, 2-4 hour seminars attract the most attendance:

So, there's a little taste of 3² factor DOE using ANOVA with the QI Macros.

ANOVA and Design of Experiments are both included in the QI Macros SPC Software for Excel.

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