Hypothesis test for paired samples in the presence of missing data

Abstract

Missing data are present in almost all statistical analysis. In simple paired design tests, when some subject has one of the involved variables missing in the so-called partially overlapping samples scheme, it is usually discarded for the analysis. The lack of consistency between the information reported in the univariate and multivariate analysis is, perhaps, the main consequence. Although the randomness on the missing mechanism (missingness completely at random) is an usual and needed assumption for this particular situation, missing data presence could lead to serious inconsistencies on the reported conclusions. In this paper, the authors develop a simple and direct procedure which allows using the whole available information in order to perform paired tests. In particular, the proposed methodology is applied to check the equality among the means from two paired samples. In addition, the use of two different resampling techniques is also explored. Finally, real-world data are analysed.

Keywords:

• missing data
• paired samples
• t-test
• Welch correction
• bootstrap method

Acknowledgements

The authors are very grateful with the Servicio de Cardiología del Hospital Universitario Central de Asturies (HUCA) and, in special, with Jesus María de la Hera for collaborating in this work and letting us the use of their data set which motivated this research. As usual, first author is also grateful with Susana Díaz-Coto for the revision of the final manuscript. The comments and suggestions of the associate editor and the three anonymous referees have improved the paper, we are grateful with them for it. This work was supported by the grant MTM2011-23204 of the Spanish Ministry of Science and Innovation (FEDER support included).