Fuzzy Median Polish algorithm for analyzing very small two-way contingency tables
Ass. Prof. Mahdi Wahhab Neamah1
Asst. teacher Skaina Shamil Jasim 2
mehdi.wahab@uokerbala.edu.iq1
Sshamil@uowasit.edu.iq 2
University of Karbala – College of Administration and Economics – Department of Statistics
Abstract:
In many studies and researches, the P-value is relied upon to ensure the correctness of the results by performing several well-known tests such as the t-test, the chi-square test, or even the ANOVA, and all these tests work under conditions that provide a normal distribution of the data. However, in very small contingency tables (very small sample size in the cells of table) these tests may not give significance to the p-value if used, despite the significance of the items used in the contingency table. Even the tests designated for such cases, which are considered robust tests for such cases, such as the Wilcoxon, Mann Whitney, and Kruskal Waleze test, may not give a statistically significant to the P-value at very small sample sizes. In most cases, the data obtained in the contingency table is inaccurate, or obtaining it is through some (unconventional) linguistic variables, so we will face the problem of inaccuracy in the data (fuzzy of data). Besides the small sample size in the cells of tables and inaccuracy in the data, we have a problem in carry out a accurate and robust analysis for such cases. In this paper, the principle of fuzzy sets was used with a method that depends on the median in analyzing the two-way contingency table whose data is very small(cells in the table very small), which is the Median Polish method, which is called the method of polishing the median, and with the use of the principle of fuzziness, we will have a method of polishing the fuzzy median Polish , an iterative algorithm that relies on the median rather than the mean and the fuzzy principle for analyzing very small cells.
Key words: Median Polish, tow way contingency tables, fuzzy sets.
