Abstract
Two different families of penalized power-divergence test statistics have been defined to find alternatives to the likelihood ratio and the Pearson chi-squared test statistics for testing linear- by-linear association in two-way contingency tables with empty cell(s). The exact size and power properties of these test statistics and the ordinary power-divergence test statistics have been studied based on an extensive designed simulation study. Different penalized test statistics have been proposed depending on their exact size and power performances.
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