Cook-Statistic for Detection of Outliers in Block Designs for Incomplete Multi-response Experiments

An incomplete multi-response experiment refers to an experimental design where not all response variables are measured for each experimental unit. This could occur due to resource limitations, time constraints, or economic considerations, leading to variations in the number of responses recorded across different experimental units. Outliers are a prevalent occurrence in data collection which if ignored can result in biased estimates and conclusions that are misleading. The partitioning of the design matrix, the variance–covariance matrix, and the normal equation becomes substantially different when handling more than two sets of data. Therefore, we have developed a methodology for the development of Modified Cook-statistic for identification of outliers for multiple sets of experimental units, each with varying numbers of response variables. A real life dataset is considered on which Modified Cook-statistic is applied for outlier detection and shown that some treatment contrast become significant while in presence of outliers they were non-significant and hence there is change in overall conclusion of the experiment.