Patterns of Means and Standard Deviations with Binary Variables: A Key to Detecting Fraudulent Research

Abstract

Heathers and his colleagues have proposed a variety of tests to detect inconsistencies in research data, including the GRIM, SPRITE, DEBIT, and RIVETS tests. Binary data are common in social science research, for such variables as male/female, rural/urban, white/nonwhite, or college educated/not college educated. However, the standard deviation for binary data is a direct mathematical function of the mean score. We show how standard deviations vary as a function of the mean and how the maximum possible standard deviation varies as a function of sample size for a mean of .50. Implications for detecting fraudulent data are discussed.

Using Statistics from Binary Variables to Detect Data Anomalies, Even Possibly Fraudulent Research

“…There will always be more complicated ways, but we try to find simpler approaches useful for a wider range of scholars (Schumm, 2018;. Figure 1 shows a plot of means and standard deviations for a binary variable when N = 100 (A plot for N = 10 is available elsewhere; see Schumm, Crawford, and Lockett, 2019). It is clear from Figure 1 that standard deviations are predicted perfectly from mean scores for binary variables.…”

A Further Examination of Excesses or Deficits of Terminal Zeroes in Scientific Research: Using Binomial Testing to Assess Probabilities for Different Anomaly Classifications as a Function of Different Sample Sizes of Coefficients with Terminal Digits

“…There are many ways to try to detect if research has been manipulated or fabricated [1,2]. In some cases, probability formulas can assist in such efforts [3].…”