Parameter estimation and model fitting underlie many statistical procedures. Whether the objective is to examine central tendency or the slope of a regression line, an estimation method must be used. Likelihood is the basis for parameter estimation, for determining the best relative fit among several statistical models, and for significance testing. In this review, the concept of Likelihood is explained and applied computation examples are given. The examples provided serve to illustrate how likelihood is relevant, and related to, the most frequently applied test statistics (Student’s t-test, ANOVA). Additional examples illustrate the computation of Likelihood(s) using common population model assumptions (e.g., normality) and alternative assumptions for cases where data are non-normal. To further describe the interconnectedness of Likelihood and the Likelihood Ratio with modern test statistics, the relationship between Likelihood, Least Squares Modeling, and Bayesian Inference are discussed. Finally, the advantages and limitations of Likelihood methods are listed, alternatives to Likelihood are briefly reviewed, and R code to compute each of the examples in the text is provided.L’estimation de paramètres et l’ajustement de modèles est au coeur de toutes procédures statistiques. Que l’objectif soit d’examiner la tendance centrale ou une pente de régression, une méthode d’estimation est nécessaire. La fonction de vraisemblance est la pierre angulaire sur laquelle repose l’estimation de paramètres, les tests d’hypothèses et la comparaison de modèles. Cet article présente le concept de vraisemblance et les tests statistiques communément utilisés (tests t, ANOVA). Certains exemples présentent le calcul de la fonction de vraisemblance lorsque le postulat de normalité est présent et lorsqu’il n’est pas adéquat. Les liens entre vraisemblance, rapport de vraisemblance, méthodes des moindres carrés et bayésienne sont discutés. Finalement, les forces et les faiblesses des méthodes basées sur la vraisemblance sont énumérées et des méthodes alternatives sont mentionnées. Des instructions en R sont données pour tester les exemples du texte.A estimativa de parâmetros e o ajustamento de modelos está no cerne de todos os procedimentos estatísticos. Se o objetivo é analisar a tendência central ou uma inclinação de regressão, é necessário um método de estimativa. A função de verossimilhança é a pedra angular sobre a qual assentam a estimativa de parâmetros, os testes de hipóteses e a comparação de modelos. Este artigo introduz o conceito de verosimilhança e os testes estatísticos vulgarmente utilizados (testes t, ANOVA). Alguns exemplos mostram o cálculo da função de verossimilhança quando o pressuposto de normalidade está presente e sempre que não é adequado. Discutem-se as ligações entre a verosimilhança, razão de verossimilhança, os métodos dos mínimos quadrados e o bayesianismo. Por fim, são enumeradas as forças e as fraquezas dos métodos baseados na verosimilhança e são mencionados os métodos alternativos. As instruções em R s...

In behavioral science research there is often the need to determine if an outcome variable differs, or is equivalent, across groups. Significance tests are the most prevalently applied data analysis method for this type of question. The purpose of this study was to examine how statistical tests for equivalence and difference have been applied to compare clinical interventions. Peer-reviewed journal articles that made treatment comparisons were examined. For each study, the primary hypothesis, statistical test usage, and the stated conclusion were recorded. Of the 270 studies investigated, 54.4% inappropriately made equivalence-based conclusions from difference-based test statistics (e.g., t test, ANOVA). Significance tests are often applied as a matter of course regardless of the research question. We have found that difference tests are similarly favored and have been applied to examine difference and inappropriately applied to examine equivalence. We discuss our findings and provide resources for researchers who want to statistically evaluate between-groups equivalence.

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