According to the description effect range, the method of scaling system in cartography is with the precision of four grades： nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have rese...According to the description effect range, the method of scaling system in cartography is with the precision of four grades： nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set （A ,≤） is the mapping of evaluation object （X, ≤） under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f（xi ） = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set （A, ≤） and evaluation object （X, ≤） is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.展开更多
There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate t...There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.展开更多
There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate t...There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.展开更多
文摘According to the description effect range, the method of scaling system in cartography is with the precision of four grades： nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set （A ,≤） is the mapping of evaluation object （X, ≤） under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f（xi ） = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set （A, ≤） and evaluation object （X, ≤） is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.
文摘There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.
文摘There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.
