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Techniques and Methods

Murine genetic models of obesity: type I error rates and the power of commonly used analyses as assessed by plasmode-based simulation



Genetic contributors to obesity are frequently studied in murine models. However, the sample sizes of these studies are often small, and the data may violate assumptions of common statistical tests, such as normality of distributions. We examined whether, in these cases, type I error rates and power are affected by the choice of statistical test.


We conducted “plasmode”-based simulation using empirical data on body mass (weight) from murine genetic models of obesity. For the type I error simulation, the weight distributions were adjusted to ensure no difference in means between control and mutant groups. For the power simulation, the distributions of the mutant groups were shifted to ensure specific effect sizes. Three to twenty mice were resampled from the empirical distributions to create a plasmode. We then computed type I error rates and power for five common tests on the plasmodes: Student’s t test, Welch’s t test, Wilcoxon rank sum test (aka, Mann–Whitney U test), permutation test, and bootstrap test.


We observed type I error inflation for all tests, except the bootstrap test, with small samples (≤5). Type I error inflation decreased as sample size increased (≥8) but remained. The Wilcoxon test should be avoided because of heterogeneity of distributions. For power, a departure from the reference was observed with small samples for all tests. Compared with the other tests, the bootstrap test had less power with small samples.


Overall, the bootstrap test is recommended for small samples to avoid type I error inflation, but this benefit comes at the cost of lower power. When sample size is large enough, Welch’s t test is recommended because of high power with minimal type I error inflation.

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Fig. 1: Summary of the simulation protocol.
Fig. 2: Summary of baseline body mass (weight).
Fig. 3: Estimated type I error rate from the plasmode-based simulation (significance level = 0.05).
Fig. 4: Summary of type I error rate for each sample size (significance level = 0.05).
Fig. 5: Estimated power with effect size set to Cohen’s d of 1.5 for each test.

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This study was supported in part by NIH grants 3P30DK056336 (DBA), R25DK099080 (DBA), R25HL124208 (DBA) and Japan Society for Promotion of Science (JSPS) KAKENHI grant 18K18146 (KE). The data analyses and simulation were performed using a supercomputer, Karst, which was supported in part by Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute, and in part by the Indiana METACyt Initiative. The Indiana METACyt Initiative at IU was also supported in part by Lilly Endowment, Inc. The opinions expressed are those of the authors and do not necessarily represent those of the NIH or any other organization. All the code which was used in this study will be available through the following webpage: Supplementary information is available at the International Journal of Obesity’s website.

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Authors and Affiliations



DBA designed the research. DLSJ and AWB gathered the data. KE and AWB performed statistical analysis. DBA, DLSJ, and UB assisted in data analysis. All authors were involved in writing or editing the paper and had final approval of the submitted and published versions

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Correspondence to Keisuke Ejima or David B. Allison.

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Conflict of interest

UB has no conflicts of interest. In the last 12 months, DBA has received personal payments or promises for same from for-profit organizations including: Biofortis; Gelesis; Fish & Richardson, P.C.; IKEA; Law Offices of Ronald Marron; Sage Publishing; Tomasik, Kotin & Kasserman LLC; Medpace; Nestle; WW (formerly Weight Watchers International, LLC) and was an unpaid member of the International Life Sciences Institute North America Board of Trustees. In the last 12 months, AWB has received personal payments or paid travel from: American Society for Nutrition, Indiana University, Kentuckiana Health Collaborative, Rippe Lifestyle Institute, Inc. Indiana University has received grants from the following entities to support some of the authors’ research or educational activities: NIH; Alliance for Potato Research and Education; American Federation for Aging Research; Dairy Management Inc; Herbalife; Laura and John Arnold Foundation; Oxford University Press; Sloan Foundation; University of Alabama at Birmingham. In the last 12 months, DLSJ has received personal payments or paid travel from: University of Alabama at Birmingham. University of Alabama at Birmingham has received grants from the following entities to support some of the authors’ research or educational activities: NIH; Alliance for Potato Research and Education. In the last 12 months, KE has received personal payments or paid travel from: The University of Tokyo. The University of Tokyo has received grants from the following entities to support some of the authors’ research or educational activities: Japan Society for the Promotion of Science.

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Ejima, K., Brown, A.W., Smith, D.L. et al. Murine genetic models of obesity: type I error rates and the power of commonly used analyses as assessed by plasmode-based simulation. Int J Obes 44, 1440–1449 (2020).

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