Analysis of Duplicated Multiple-Samples Rank Data Using the Mack-Skillings Test

Abstract

© 2016 Institute of Food Technologists® Appropriate analysis for duplicated multiple-samples rank data is needed. This study compared analysis of duplicated rank preference data using the Friedman versus Mack-Skillings tests. Panelists (n = 125) ranked twice 2 orange juice sets: different-samples set (100%, 70%, vs. 40% juice) and similar-samples set (100%, 95%, vs. 90%). These 2 sample sets were designed to get contrasting differences in preference. For each sample set, rank sum data were obtained from (1) averaged rank data of each panelist from the 2 replications (n = 125), (2) rank data of all panelists from each of the 2 separate replications (n = 125 each), (3) jointed rank data of all panelists from the 2 replications (n = 125), and (4) rank data of all panelists pooled from the 2 replications (n = 250); rank data (1), (2), and (4) were separately analyzed by the Friedman test, although those from (3) by the Mack-Skillings test. The effect of sample sizes (n = 10 to 125) was evaluated. For the similar-samples set, higher variations in rank data from the 2 replications were observed; therefore, results of the main effects were more inconsistent among methods and sample sizes. Regardless of analysis methods, the larger the sample size, the higher the χ(2) value, the lower the P-value (testing H0 : all samples are not different). Analyzing rank data (2) separately by replication yielded inconsistent conclusions across sample sizes, hence this method is not recommended. The Mack-Skillings test was more sensitive than the Friedman test. Furthermore, it takes into account within-panelist variations and is more appropriate for analyzing duplicated rank data.