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A test of independence is commonly used to determine differences (or associations) between samples in a nominal level measurement. Fisher’s exact test and Chi-square test are two of the most widely applied tests of independence used in the data analyses in different areas such as information technologies, biostatistics, psychology and health sciences. In some cases, contingency tables with null entries (also called random zeros) arise, particularly if the number of samples is small, and the variables analyzed are multilevel. This situation becomes a problem because if one or more entries in a contingency table are zero or have small values, then the tests of independence produce unreliable results. In this paper, we propose a method to address that issue. The method merges one or more levels of the variables analyzed to create contingency tables with only one degree of freedom, avoiding applying a test of independence on contingency tables with random zeros. The source code (Python) of the method is publicly available for use. The results obtained using our method give a complete panorama of the associations between the variables of a data set. To show the effectiveness of our approach to find dependencies between variables, we use four data sets publicly available on the Internet.

Data warehousing gives frameworks and means for enterprise administrators to methodically prepare, comprehend, and utilize the data to improve strategic decision-making skills. One of the principal challenges to data warehouse designers is fragmentation. Currently, several fragmentation approaches for data warehouses have been developed since this technique can decrease the OLAP (online analytical processing) query response time and it provides considerable benefits in table loading and maintenance tasks. In this paper, a horizontal fragmentation method, called FTree, that uses decision trees to fragment data warehouses is presented to take advantage of the effectiveness that this technique provides in classification. FTree determines the OLAP queries with major relevance, evaluates the predicates found in the workload, and according to this, builds the decision tree to select the horizontal fragmentation scheme. To verify that the design is correct, the SSB (star schema benchmark) was used in the first instance; later, a tourist data warehouse was built, and the fragmentation method was tested on it. The results of the experiments proved the efficacy of the method.