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The problem is not statistics per se, but the 'penis envy" of a sort - or a desire to achieve the rigor of natural science. This results in mimicking the procedures of natural sciences, especially use of mathematical/statistical procedures. This natural science "penis envy" leads to a fundamental distortion in which scientists disregard forming a priori conceptual models and testing them with probabilistic procedures, but instead of use probabilistic "data dredging" to find anything significant and then manufacture conceptual models a posteriori to fit the accidental findings.
This problem is greatly exacerbated by the intellectual property rights culture that dominates the academia. Scientists "own" the results in the same way a fiction writer owns her prose - they create them ex nihilo and sell them in exchange of careers or even pecuniary rewards.
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