Reviewers of research reports frequently criticize the choice of statistical methods. While some of these criticisms are well-founded, frequently the use of various parametric methods such as analysis of variance, regression, correlation are faulted because: (a) the sample size is too small, (b) the data may not be normally distributed, or (c) The data are from Likert scales, which are ordinal, so parametric statistics cannot be used. In this paper, I dissect these arguments, and show that many studies, dating back to the 1930s consistently show that parametric statistics are robust with respect to violations of these assumptions. Hence, challenges like those above are unfounded, and parametric methods can be utilized without concern for “getting the wrong answer”.
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Representativeness is required of all statistical tests and is fundamental to statistical inference. But it is unrelated to sample size.
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Norman, G. Likert scales, levels of measurement and the “laws” of statistics. Adv in Health Sci Educ 15, 625–632 (2010). https://doi.org/10.1007/s10459-010-9222-y