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Researchers are often faced with analyzing data sets that are not complete. To properly analyze such data sets requires the knowledge of the missing data mechanism. If data are missing completely at random (MCAR), then many missing data analysis techniques lead to valid inference. Thus, tests of MCAR are desirable. The package MissMech implements two tests developed by Jamshidian and Jalal (2010) for this purpose. These tests can be run using a function called TestMCARNormality. One of the tests is valid if data are normally distributed, and another test does not require any distributional assumptions for the data. In addition to testing MCAR, in some special cases, the function TestMCARNormality is also able to test whether data have a multivariate normal distribution. As a bonus, the functions in MissMech can also be used for the following additional tasks: (i) test of homoscedasticity for several groups when data are completely observed, (ii) perform the k-sample test of Anderson-Darling to determine whether k groups of univariate data come from the same distribution, (iii) impute incomplete data sets using two methods, one where normality is assumed and one where no specific distributional assumptions are made, (iv) obtain normal-theory maximum likelihood estimates for mean and covariance matrix when data are incomplete, along with their standard errors, and finally (v) perform the Neyman’s test of uniformity. All of these features are explained in the paper, including examples.