Latin Squares with Missing Data

If one observation is missing in a Latin Squares design, its value can be estimated using the following formula, where the means are taken excluding the missing value:

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For example, if cell B6 is missing from the data for Example 1 of Latin Squares Design, then, as we can see from Figure 1, we can estimate the missing data element as

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Latin Squares marginal totals

Figure 1 – Marginal totals for missing data

Using this value, we arrive at the analysis shown in Figure 2. Notice too that we have reduced the Error and Total degrees of freedom terms by 1 to account for the missing data value.

Latin Squares imputed data

Figure 2 – Latin Squares design with imputed missing data

Most of the values in Figure 2 are not much different from those in Figure 4 of Latin Squares Design, but the reduced degrees of freedom for the Error term changes the Treatment test from significant to not significant.

4 thoughts on “Latin Squares with Missing Data”

  1. Charles,
    I have a question for you the ANOVA based on the imputed value. As one record is imputed, do we need to adjust the df for total and error terms to reflect the missing cell and conduct the Anova based on the adjusted MSE?

    -Sun

    Reply
    • Hello Sun,
      Yes, you are correct. The df and MSE need to be adjusted to account for the missing data element. I am going to review Latin Squares with missing data based on an article I am reading at the following website and I will then make the necessary changes to the Real Statistics website and software.
      Charles

      Reply

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