Level: Beginner
When trying to analyze real data with two qualitative variables and a quantitative variable as a response, it inevitably results in a "two-way layout with uneven repetitions," but I cannot find any textbooks in Japanese that deal with this issue. Perhaps because of this, on the web, statements such as "analysis is not possible unless the repetitions are equal" are rampant. The reason for this is that analytical methods that rely solely on decomposition of sums of squares and use a design matrix X with dummy variables are frowned upon introductory statistics books. JMP users who use "fit model" should be able to analyze without worrying at all whether the repetitions are equal or uneven. When trying to find the level average of a qualitative variable in "Effect details," the "least squares mean" and "average" are output, and you must be aware that there is a discrepancy between them. However, is it possible to clearly explain the difference? Here, we will show a method of analysis using Excel's matrix functions for 2x3 repeated, unbalanced two-way data, and by comparing it with the analysis results using JMP, we will show an alternative calculation method to sum-of-squares decomposition to deepen understanding of the calculation principles of "model fitting" and enable further applications.
I have been using SAS since before JMP4. At my previous company, I was engaged in various statistical education using JMP and promoted JMP within the company. I introduced the results of this at JMPer's meetings from time to time. After retirement, I established a self-employed consulting company and continue to work there. Recently, I have realized that the ability to analyze real data statistically in many academic fields in Japan (except clinical statistics) is declining collectively. For me, experimental design was essential for learning statistical theory and applying it in practice. Although the theme of this issue was a problem I had already solved, when I reread books related to experimental design, I was shocked to see that there were no examples using the calculation principle of JMP's "model fitting" and there was a parade of traditional analysis methods that stuck to the classical sum-of-squares decomposition. I became convinced that this was the widespread delusion that it was impossible to analyze repeated, uneven two-way data.
