The A Priori Procedure for estimating the mean in both log-normal and gamma populations and robustness for assumption violations

• Published in: Methodology Vol. 18; no. 1; pp. 24 - 43
• Main Authors: Cao, Lixia, Tong, Tingting, Trafimow, David, Wang, Tonghui, Chen, Xiangfei
• Format: Journal Article
• Language: English
• Published: PsychOpen GOLD/ Leibniz Institute for Psychology 31.03.2022
• Subjects: a priori procedure; gamma distribution; log-normal distribution; minimum sample size; robustness; skew normal
• DOI: 10.5964/meth.7321
• ISSN: 1614-2241

Although the literature on the a priori procedure, designed to help researchers determine the sample sizes they should use in their substantive research, is expanding rapidly, there are two important limitations. First, there is a need to expand to new popular distributions, log-normal and gamma distributions, and the present work provides those expansions. Second, there is a need to test the consequences of wrong distributional assumptions; for example, assuming a log-normal distribution when the population follows a gamma distribution, or the reverse. The present work addresses the limitations with respect to estimating population means, and it includes computer simulations, links to free and user-friendly programs that researchers can utilize for their own research, and two examples involving real data sets for illustrations of our main results.