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

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 χ2 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. Practical Application Analyses of duplicated rank preference data using the Friedman versus Mack–Skillings tests were compared. Panelists ranked twice 2 orange juice sets: different-samples set (100%, 70%, vs. 40% juice) and similar-samples set (100%, 95%, vs. 90%). 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 (n = 10 to 125). Analyzing rank data separately by replication yielded inconsistent conclusions across sample sizes, hence it is not recommended. The Mack–Skillings test is more sensitive than the Friedman test, and more appropriate for analyzing duplicated rank data.