Archive image from page 11 of Definition and use of the. Definition and use of the phi grade scale definitionuseofp00hobs Year: 1979 classes produces a systematic and logical division of particle sizes, this same property can also create some unique problems for the statis- tical analysis and graphing of size data. In statistics, sample size often affects analysis results; therefore, it is desirable to have a size scale with class limits that can be easily halved or quartered in order to provide an adequate number of experimentally determined points for analytic purposes. Geometric scales ca
Archive image from page 11 of Definition and use of the. Definition and use of the phi grade scale definitionuseofp00hobs Year: 1979 classes produces a systematic and logical division of particle sizes, this same property can also create some unique problems for the statis- tical analysis and graphing of size data. In statistics, sample size often affects analysis results; therefore, it is desirable to have a size scale with class limits that can be easily halved or quartered in order to provide an adequate number of experimentally determined points for analytic purposes. Geometric scales can be subdivided into smaller equal-sized classes but the class limits produced are often irrational rather than of integer value and more difficult to handle quantita- tively. An arithmetic-size scale would be easy to subdivide and could be derived from an existing geometric scale through the use of an appropriate logarithmic transformation. Graphing techniques are commonly used for comparing the grain-size distributions Cgsd) of different sediment samples. Plots of cumulative proportion (usually weight percent) of sediment coarser than a series of size classes tend to be fairly straight and steep in the less than 1-millimeter class size, and then to 'tail out' toward the coarser sizes. The shapes of plots for different sample gsds might appear similar even though there are important textural differences. If the differences occur in the finer sizes, this kind of diagram tends to push these sizes together rather than to accentuate them (Fig. l,a). This graphing prob- lem, like the statistical problem above, could also be solved by using logarithms to transform the geometric-size scale into an arithmetic scale. 2 I 0 Groin Size (mm) -2 0 12 3 Gram Size((/)) Figure 1. Cumulative size-frequency plots comparing (a) millimeter and (b) phi-size scales. 2. Phi Grade Scale. The phi notation, introduced by Krumbein (1934, 1958), is used to transform the geometric VVentworth scale
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