Statistical Papers https://doi.org/10.1007/s00362-019-01098-8 REGULAR ARTICLE Power calculation in multiply imputed data Ruochen Zha 1 · Ofer Harel 1 Received: 7 September 2017 / Revised: 20 December 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract Multiple imputation (MI) has been proven an effective procedure to deal with incom- plete datasets. Compared with complete case analysis (CCA), MI is more efficient since it uses the information provided by incomplete cases which are simply discarded in CCA. A few simulation studies have shown that statistical power can be improved when MI is used. However, there is a lack of knowledge about how much power can be gained. In this article, we build a general formula to calculate the statistical power when MI is used. Specific formulas are given for several different conditions. We demonstrate our finding through simulation studies and a data example. 1 Introduction Power calculation plays an important role in data analysis and experiment design. Statistical power is defined as the probability of correctly rejecting a null hypothesis, therefore evaluating the likelihood of detecting a statistically significant effect when it is there (Balkin and Sheperis 2011). Knowing the statistical power of a hypoth- esis test can help increase research efficiency, guide research design and estimate required sample size (Steidl et al. 1997). To date, most funding agencies, including National Institutes of Health (NIH) and National Aeronautics and Space Administra- tion (NASA), require a power calculation segment in their grant application. In general, there are two different methods to calculate statistical power: closed- form formula and simulation. Usually, researchers can compute their statistical power using tables or closed-form formulas provided by textbooks such as the Murphy et al. (1998) and Cohen (1988). This method requires researchers to provide significance level α, effect size, and sample size and has been implemented in most standard statistic softwares like SAS (SAS Institute Inc. 2011), R (R Core Team 2015), SPSS (IBM Corp. 2013), etc. As an alternate, Monte Carlo simulation has also been recommended, espe- cially when it is impractical to obtain the closed-form formula (der Sluis S et al. 2008). B Ofer Harel ofer.harel@uconn.edu 1 The University of Connecticut, Storrs, USA 123