This paper presents a data set based on an industrial case study using design of experiments. The data set is pedagogically rich because it has a rather large total sample size from an industrial setting that naturally yields a large third order interaction term. The experiment is a 23 design and is initially presented with no replications. The sample size of the data is then doubled and the analysis repeated, comparing these results with previous results. The process is repeated until eight replications are available for each combination of factors and all parameters are estimated. With eight replications, the analysis shows all main effects and all interactions are statistically significant at the a = 0.05 level. With smaller sample sizes, various main effects and interactions are not found to be statistically significant. Through this presentation the instructor can lead students in discussions about the effect of increased sample sizes, power, statistical significance (or insignificance), interaction terms, Type I and Type II errors as well as the importance and the role of the error term. In addition, students can manipulate the data set in a computer laboratory setting to illustrate many of the concepts inherent in the design of experiments and analysis of variance.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education