Measurement of peakedness in variables on nominal scale

Abstract

The objective of this methodological study is to define and develop a qualitative peakedness measure and to test its validity. One hundred twenty qualitative distributions were generated from binomial distributions. The percentile kurtosis and the average of five judges when visually assessing the degree of peakedness were used as validity criteria. Peakedness was defined as the standout of the peak between the shoulders. From the frequencies of the nominal categories, it was specified how to chart a bar diagram and measure the distance from the peak to the shoulders. The statistic showed a behavior adjusted to expectations. Its correlation with average inter-judge peakedness was .87 and with percentile kurtosis ?.38. It is concluded that a concept of qualitative peakedness can be defined and measured reliably.