Dears,
I want to conduct a research about composite materials. in my work I have 5 parameters with 4 levels but the problem is that some of the parameters have only two or three levels (see table attached). the question is, can I assume the missing levels and construct orthogonal array based on the assumed levels. then during experimental work I will neglect any rows contain the assumed levels. would this assumption affects adversely on the SN ratio and ANOVA analysis accuracy.
regards
You can do listwise deletion - omit those cases with missing data and run the analyses on what remains.
I found this:
"By far the most common approach to missing data is to simply omit those cases with missing data and to run our analyses on what remains. Thus if 5 subjects in Group 1 don't show up to be tested, that group is 5 observations short. Or if 5 individuals have missing scores on one or more variables, we simply omit those individuals from the analysis. This approach is usually called listwise deletion, but it is also known as complete case analysis.
Although listwise deletion often results in a substantial decrease in the sample size available for the analysis, it does have important advantages. In particular, under the assumption that data are missing completely at random, it leads to unbiased parameter estimates. Unfortunately, even when the data are missing completely at random (MCAR) there is a loss in power using this approach, especially if we have to rule out a large number of subjects. And when the data are not MCAR, bias results (for example when low income individuals are less likely to report their income level, the resulting mean is biased in favor of higher incomes)".
Ahmed Taifor
Mixed orthogonal arrays can be used for the case defined by you.
Mixed orthogonal arrays allows to study few factors at certain levels and few factors at other levels.
Few examples of mixed OA are:
L18 OA (2^1 x 3^7) = One factor at 2 levels and seven factors at 3 levels can be studied
L'32 OA (2^1 x 4^9) = One factor at 2 levels and nine factors at 4 levels can be studied
L36 OA (2^11 x 3^12) = Eleven factors at 2 levels and twelve factors at 3 levels can be studied
L'36 OA (2^3 x 3^13) = Three factors at 2 levels and thirteen factors at 3 levels can be studied
L50 OA (2^1 x 5^11) = One factor at 2 levels and eleven factors at 5 levels can be studied
L54 OA (2^1 x 3^25) = One factor at 2 levels and twenty five factors at 3 levels can be studied
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