Imputation or likelihood-based approaches to handle missing data assume the data are missing completely at random (MCAR) or missing at random (MAR). However, little research has examined the missingness pattern before using these imputation/likelihood methods. Three missingness mechanisms -- MCAR, MAR, and not missing at random (NMAR) -- can be tested using information on research design, disciplinary knowledge, and appropriate methods. This study summarized six commonly used statistical methods to test the missingness mechanism and discussed their application conditions. We further applied these methods to a two-wave longitudinal dataset from the Health and Retirement Study (N = 18,747). Health measures met the MAR assumptions although we could not completely rule out NMAR. Demographic variables provided auxiliary information. The logistic regression method demonstrated applicability to a wide range of scenarios. This study provides a useful guide to choose methods to test missingness mechanisms depending on the research goal and nature of the data.