Interlaboratory comparison of the intensity of drinking water odor and taste by two-way ordinal analysis of variation without replication

Abstract

A case study of ordinal data from human organoleptic examination (sensory analysis) of drinking water obtained in an interlaboratory comparison of 49 ecological laboratories is described. The recently developed two-way ordinal analysis of variation (ORDANOVA) is applied for the first time for the treatment of responses on the intensity of chlorine and sulfurous odor of water at 20 and 60 °C, which is classified into the six categories from ‘imperceptible’ to ‘very strong’. The one-way ORDANOVA is used for the analysis of the ‘salty taste’ intensity of the water. A decomposition of the total variation of the ordinal data and simulation of the multinomial distribution of the data-relative frequencies in different categories allowed the determination of the statistical significance of the difference between laboratories in classifying chlorine or sulfurous odor intensity by categories, while the effect of temperature was not significant. No statistical difference was found between laboratories on salty taste intensity. The capabilities of experts to identify different categories of the intensity of the odor and taste are also evaluated. A comparison of the results obtained with ORDANOVA and ANOVA showed that ORDANOVA is a more useful and reliable tool for understanding categorical data such as the intensity of drinking water odor and taste.

Power of a test for assessing interlaboratory consensus of nominal and ordinal characteristics of a substance, material, or object

“…Such decomposition may include a component related to the possible interaction between the two factors. In addition, decomposition by response categories was discussed in papers [20][21][22]. Note that the sample estimators by equations ( 2)-( 9) are biased from the corresponding population variations [41,43].…”

“…The proposed algorithm using random Monte Carlo draws from a multinomial distribution was applied for example with ordinal variables for evaluation of power of the consensus of 45 laboratories participated in an interlaboratory comparison of the intensity of chlorine and sulfurous odors of different drinking water samples [21]. The laboratory responses, classified into six categories, were obtained for each water sample at 20 and 60 • C. Thus, there were: factor X1-laboratory with I = 45 levels; factor X2 -temperature of a water sample with J = 2 levels; K = 6 categories/levels of chlorine or sulfurous odor intensity; n = 1 -one response from each laboratory related to a sample of the specified odor at the specified temperature; N = IJ = 90 responses in total for each chlorine odor and sulfurous odor.…”

“…Categorical variables are nominal/qualitative or ordinal/semi-quantitative. For example, kinds of weld imperfections [20] and descriptors of water odor [21] are nominal variables, whose occurrences can be only equal or unequal, i.e. can belong to the same or different categories.…”

“…Consensus of responses of different laboratories participating in an interlaboratory comparison, classifying a substance, material, or object according to its nominal and ordinal characteristics, could be also interpreted as cohesiveness. The recently developed two-way factorial analysis of variation of nominal variables CATANOVA and of ordinal variables ORDANOVA, applied first in [20] and [21][22][23], respectively, answers the question' is a consensus among participating laboratories achieved?' The answer is based on testing hypotheses about homogeneity of the between-laboratory and within-laboratory variation components, as well as the components caused by other factors under study.…”

Ordinal Analysis of Variation of Sensory Responses in Combination with Multinomial Ordered Logistic Regression vs. Chemical Composition: A Case Study of the Quality of a Sausage from Different Producers

“…When the cumulative relative frequencies in (7) achieve 1, the variation 􏽢 C B (􏽐 k l�1 Y l ) � 0. Tis is always the case for the last category K, but may also be for (K -1) or even for (K -2) [26], depending on the form of the cumulative distribution function.…”