STATISTICA & APPLICAZIONI - 2005 - 1

This paper proposes, for ordinal variables, a new type of mean called bipolar mean, that is a frequency distribution with the total size n concentrated on one category or on two consecutive categories. The bipolar mean is coherent with the usual statistics dominance that is based on the retro-cumulative frequencies. The paper shows that the number of bipolar means that it is possible to get for the frequency distributions with k categories and total size n is nk –n+1. Note that the traditional means utilised for ordinal variables (the median and the mode) take only k categories. Two applications are presented to show how the BM works.

In this paper we compare the accuracy of three packages that are commonly used for statistical calculations: Excel of Microsoft, version XP Edition 2003, Statistica of Statsoft, version 6, and R, an open-source free software, available on the web, version 1.9.0. To assess the accuracy of each software in different statistical areas, we are going to use benchmarks expressly developed for this aim. The obtained results show a superiority of R in comparison with the other two softwares.

This work presents a continuous characters classification tecnique, which satisfies some optimality criterion, such as the maximisation of the variance “between” or the minimisation of the concentration “within” the groups, measured by some index which admits a decomposition. Such a tecnique is based on an algorithm which gives all the possible frequency distributions with fixed sum, the way that each class is not empty. As the algorithm is exponential, it is necessary to impose the minimum number of statistical units per class, which fact implies the construction of two classes of residual statistical units, to the left and to the right. In order to have indications about the optimal number of classes, the minimum number of statistical units per class, and about the imputation of the residual statistical units to the left and the right class, the tecnique will be applied to classify a 13868 individual income sample, drawn by Italian Bank in 1991.

Randomized response is a method used in statistical surveys whose goal is to reduce or eliminate respons errors which occour when respondents are queired about sensitive or highly personal matters. In this work the goals are to analyze and compare the respondent privacy protection in some randomized response models according to efficiency and privacy protection. We prove that some single and double randomization models give no advantage in terms of efficiency under the condition of equal respondent protection compared to Warner’s and Simmons’ models.