We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable.

The main goal of this paper is to examine Nobel Prize data by studying the association among the laureate’s country of birth or residence, discipline, time period in which the Nobel Prize was awarded, and gender of the recipient. Multiple correspondence analysis is used as a tool to examine the association between these four categorical variables by cross classifying them in the form of a four-way contingency table. The data that we examine comprise Nobel Prize recipients from 1901 to 2018 (inclusive) from eight-developed countries, with a total sample of 785 Nobel Prize recipients. The countries include Canada, France, Germany, Italy, Japan, Russia, the British Isles, and the USA and the disciplines in which the individuals were awarded the prizes include chemistry, physics, physiology or medicine, literature, economics, and peace.

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The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display—the polynomial biplot.