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Hodges, C.B., Stone, B.M., Johnson, P.K., Carter III, J.H, Sawyers, C.K., Roby, P.R. and Lindsey, H.M. (2023) Researcher Degrees of Freedom in Statistical Software Contribute to Unreliable Results: A Comparison of Nonparametric Analyses Conducted in SPSS, SAS, Stata, and R. Behavior Research Methods, 55, 2813-2837.
https://doi.org/10.3758/s13428-022-01932-2

has been cited by the following article:

• TITLE: Calculation of Two-Tailed Exact Probability in the Wald-Wolfowitz One-Sample Runs Test

  AUTHORS: José Moral De La Rubia

  KEYWORDS: Randomness, Nonparametric Test, Exact Probability, Small Samples, Quantiles

  JOURNAL NAME: Journal of Data Analysis and Information Processing, Vol.12 No.1, February 22, 2024

  ABSTRACT: The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n0 (number of zeros) and n1 (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.