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:
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
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.
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.
Thank You. It helped me alot
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
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
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 URL and I will then make the necessary changes to the Real Statistics website and software.
https://www.cogentoa.com/article/10.1080/23311916.2017.1411222
Charles