A note regarding problems with interaction and varying block sizes in a comparison of endotracheal tubes

A randomized clinical experiment to compare two types of endotracheal tubes utilized a block design where each of the six participating anesthesiologists performed tube insertions for an equal number of patients for each type of tube. Five anesthesiologists intubated at least three patients with each tube type, but one anesthesiologist intubated only one patient per tube type. Overall, one type of tube outperformed the other on all three effectiveness measures. However, analysis of the data using an interaction model gave conflicting and misleading results, making the tube with the better performance appear to perform worse. This surprising result was caused by the undue influence of the data for the anesthesiologist who intubated only two patients. We therefore urge caution in interpreting results from interaction models with designs containing small blocks.