Non-normal Distributions Commonly Used in Health, Education, and Social Sciences: A Systematic Review

Abstract

Statistical analysis is crucial for research and the choice of analytical technique should take into account the specific distribution of data. Although the data obtained from health, educational, and social sciences research are often not normally distributed, there are very few studies detailing which distributions are most likely to represent data in these disciplines. The aim of this systematic review was to determine the frequency of appearance of the most common non-normal distributions in the health, educational, and social sciences. The search was carried out in the Web of Science database, from which we retrieved the abstracts of papers published between 2010 and 2015. The selection was made on the basis of the title and the abstract, and was performed independently by two reviewers. The inter-rater reliability for article selection was high (Cohen’s kappa = 0.84), and agreement regarding the type of distribution reached 96.5%. A total of 262 abstracts were included in the final review. The distribution of the response variable was reported in 231 of these abstracts, while in the remaining 31 it was merely stated that the distribution was non-normal. In terms of their frequency of appearance, the most-common non-normal distributions can be ranked in descending order as follows: gamma, negative binomial, multinomial, binomial, lognormal, and exponential. In addition to identifying the distributions most commonly used in empirical studies these results will help researchers to decide which distributions should be included in simulation studies examining statistical procedures.

Natural Brain-Inspired Intelligence for Non-Gaussian and Nonlinear Environments with Finite Memory

“…We should mention here that many AI applications [14][15][16][17][18][19][20] are for NGNLEs. For example, most data obtained or measured from health conditions, education, and social sciences are often not normally distributed [14].…”

“…We should mention here that many AI applications [14][15][16][17][18][19][20] are for NGNLEs. For example, most data obtained or measured from health conditions, education, and social sciences are often not normally distributed [14]. Some examples of non-Gaussian distribution for health conditions, education, and social sciences are prostate cancer modeling [15,16], psychometrics [17], and labor income [18], respectively.…”

Bias, Precision, and Accuracy of Skewness and Kurtosis Estimators for Frequently Used Continuous Distributions

“…In a recent systematic review, Bono et al [11] found that the most widely used distributions in health, education, and social sciences can be ranked in descending order as follows: gamma, negative binomial, multinomial, binomial, lognormal and exponential.…”

“…To this end we conducted a Monte Carlo simulation study to estimate the skewness and kurtosis of the most frequent continuous distributions of the exponential family (gamma, lognormal and exponential), according to Bono et al [11]. The indicators used to assess the bias, precision and accuracy of the different estimators of skewness and kurtosis were, respectively, the relative bias (RB), the coefficient of variation (CV) and the scaled root mean square error (SRMSE).…”

Reaction times and other skewed distributions: problems with the mean and the median

“…Distributions of reaction times (RT) and many other quantities in social and life sciences are skewed (asymmetric) (Micceri, 1989;Limpert, Stahel & Abbt, 2001;Bono, Blanca, Arnau & Gómez-Benito, 2017). This asymmetry tends to differ among experimental conditions, such that a measure of central tendency and a measure of spread are insufficient to capture how conditions differ (Balota & Yap, 2011;Trafimow, Wang & Wang, 2018).…”