Can an orthogonal table be created with two factors and four levels?
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Can an orthogonal experiment be conducted with two factors and four levels? Are there only the formats provided by software for creating orthogonal tables, and is it not possible to create orthogonal tables for other numbers of factors and levels? Thank you all for your help
It is possible to make them orthogonal; please refer to the lecture notes on orthogonal experiments. I won’t mention the specific title of the book. Basically, any book on orthogonal experiments contains relevant information. In fact, it’s better to design the orthogonal arrangement by oneself – relying solely on software isn’t very effective. That’s just my personal opinion
Can you tell me directly how many sets I can do?
A good software option is Mintab; it can be searched for and downloaded online. When I conduct experiments, I try to use two levels for each factor, as this reduces the number of tests required. Generally, the number of test groups equals the square of the number of levels per factor; in the case of two factors with four levels each, that results in 16 groups
The purpose of conducting orthogonal experiments is to reduce the number of experiments. For a setup with two factors and four levels, there would be 16 groups anyway
The number of levels in an orthogonal experiment cannot exceed the number of factors. . . There is an experiment with two factors and four levels. . But there is no two-factor, four-level orthogonal experiment
It’s possible to conduct orthogonal experiments; I remember doing that during my school days. You can refer to the lecture notes on orthogonal experiments, or you can use some software as well
There is no such orthogonal table. Factors and levels are akin to the columns and rows in a matrix; when there are more rows than columns, the excess rows are eliminated during matrix simplification (at this point, the number of rows is ≤ the number of columns), and once it is reduced to an identity matrix, it can then be transformed into an orthogonal matrix. Using such a metaphor may not be entirely accurate, but it can help with understanding. However, if an orthogonal approach is to be used, that’s also possible; it is nested within a higher-order orthogonal table (a 4*4 table can be used), which is essentially a higher-order orthogonal table.