We investigate Tukey's One Degree of Freedom test for non-additivity (interaction) when there is only one entry per cell in the 2-way anova design. Following the logic and presentation by Milliken and Johnson (1989), we solve the problem for the `sorghum` dataset using R and then simplify and re-solve the problem using the R package `dae` (Brien, 2016).

Repeated measures data arise in a wide array of different research environments. The term "repeated" is used here to describe measurements that "are made on the same characteristic on the same observational unit but on more than one occasion." (Crowder and Hand, 1990, p. 1) Because the measurements for a particular individual, subject, patient or observational unit are repeated, they are not independent within the individual. Therefore, special care must be taken in the statistical analysis of such data. We analyze some _repeated measures_ data taken from the textbook by Crowder and Hand (1990), Example 3.3 on page 32.

Repeated measures data arise in a wide array of different research environments. The term "repeated" is used here to describe measurements that "are made on the same characteristic on the same observational unit but on more than one occasion." (Crowder and Hand, 1990, p. 1) Because the measurements for a particular individual, subject, patient or observational unit are repeated, they are not independent within the individual. Therefore, special care must be taken in the statistical analysis of such data. We analyze some repeated measures data taken from the textbook by Crowder and Hand (1990), Example 3.3 on page 32.

Repeated measures data arise in a wide array of different research environments. The term "repeated" is used here to describe measurements that "are made on the same characteristic on the same observational unit but on more than one occasion." Because the measurements for a particular individual, subject, patient or observational unit are repeated, they are not independent within the individual. Therefore, special care must be taken in the statistical analysis of such data. We analyze some data taken from the textbook by Crowder and Hand (1990), Example 3.3 on page 32.

A common problem in contingency table analysis is to find relationships between variables in an I x J contingency table, where either I or J, or both, are greater than 2. The problem here is to partition, or decompose, a 5 x 2 contingency table in a statistically rigorous way to describe similarities and differences between the variables in the table. The decomposition involves partitioning the table and its corresponding Likelihood Ratio Chi-Square statistic, LR \chi^{2} into orthogonal, additive components.