Attila I. Engloner (2012): Alternative ways to use and evaluate Kohler's ordinal scale to assess aquatic macrophyte abundance. Ecological Indicators 20: 238-243.
Abstract
To assess numerical information on the aquatic vegetation of running water bodies, the ‘Kohler method’, a five-level descriptor scale estimating the relative abundance of species in river sections as survey units has been frequently used. Although this scale is ordinal without any information on differences between the states, data are often evaluated by arithmetic operations as if they were on the ratio scale. Metrizing ordinal information may facilitate correct data evaluation; however, the outcome highly depends on mathematical procedures applied to the data set.
This paper demonstrates that if ordinal data are analyzed by ordination methods suited to this scale type, then results primarily reflect presence/absences. To the contrary, additional information was added to Kohler's scale when the applied analyses used values on ratio scales; therefore they provided inappropriate data evaluation.
Abstract
To assess numerical information on the aquatic vegetation of running water bodies, the ‘Kohler method’, a five-level descriptor scale estimating the relative abundance of species in river sections as survey units has been frequently used. Although this scale is ordinal without any information on differences between the states, data are often evaluated by arithmetic operations as if they were on the ratio scale. Metrizing ordinal information may facilitate correct data evaluation; however, the outcome highly depends on mathematical procedures applied to the data set.
This paper demonstrates that if ordinal data are analyzed by ordination methods suited to this scale type, then results primarily reflect presence/absences. To the contrary, additional information was added to Kohler's scale when the applied analyses used values on ratio scales; therefore they provided inappropriate data evaluation.
Four different conversion methods (the use of 1–5 values, the third power, the mean values of Braun-Blanquet cover classes and the replacement of ordinal states by ranks) were applied to reveal how the conversion procedures determine the intervals between the substituting metric values and the level of importance given to species frequency and abundance. When ordinal scale was substituted by numbers 1–5 and ranks, frequency of species was taken greatly into account. After cubic conversion the large values became considerably overemphasized, therefore species occurring in a few (or very few) survey units with high abundance values were considered more dominant than less abundant but frequently present ones. The mean values of Braun-Blanquet's cover classes gave large ordinal scores and the frequent species to have substantive representation.
The results demonstrate that conscious choice of intervals between the scores is inevitable; otherwise one generates unknown or misleading differences in species abundance. Although every researcher assessing aquatic macrophytes by Kohler's method surely has an idea on the differences between the applied scores, the use of identical, widely accepted scale substitution is prerequisite for reliable comparison.
Keywords
Macrophyte indices, Metrizing ordinal information, Ordinal scale, River ecosystems
The results demonstrate that conscious choice of intervals between the scores is inevitable; otherwise one generates unknown or misleading differences in species abundance. Although every researcher assessing aquatic macrophytes by Kohler's method surely has an idea on the differences between the applied scores, the use of identical, widely accepted scale substitution is prerequisite for reliable comparison.
Keywords
Macrophyte indices, Metrizing ordinal information, Ordinal scale, River ecosystems
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