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Several statistical tests can be used to test the MCAR assumption. Testing which of the three missingness mechanisms apply However, because of its name, MAR may easily be misinterpreted as what would technically be MCAR (see, e.g., Baraldi & Enders, 2010, p. Under MAR, missing data may be more frequent in some subgroups in the data than in others, but information defining the subgroups is observed for all respondents (gender in the example). It is important to realize that the term missing at random does not mean that the missing data are a simple random subsample of all the data points. For a more formal explanation of missingness mechanisms, see Van Buuren (2012) and Little and Rubin ( 2002). 48 see also Vach, 1994 White & Carlin, 2010) does listwise deletion give unbiased results of statistical analyses. Only in very specific and rare cases of NMAR (Van Buuren, 2012, p. However, under MAR the causes of this systematic dropout can be traced, whereas under NMAR they cannot. In general, under NMAR, listwise deletion has the same problem as it has under MAR, because there are systematic differences between the deleted cases and the cases that are left (respondents with systematically higher incomes in the preceding example). If, for example, respondents with higher incomes are more inclined to skip a question about income compared to those with low incomes, the missing data on income are NMAR. As a result, statistical inferences from analyses that include gender or variables that are related to gender may be biased.įinally, under NMAR, the probability of missingness depends on data that are not observed. In the preceding example, females are underrepresented in the leftover sample. If listwise deletion is applied under MAR, the leftover sample may not be representative of the total population anymore, consequently leading to biased results. For example, suppose that females skip a question about income more frequently than males, and gender is observed for all respondents.
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Under MAR, missing data depend on observed data but not on unobserved data. In short, under MCAR, listwise deletion reduces the sample size and by the latter, power, but does not give any biased results. Consequently, when a simple random subsample is removed from the total sample, the resulting leftover sample is still as representative of the population as the original sample was. Under MCAR, cases with missing data are a simple random subsample from all cases in the data. An example of MCAR is a respondent accidentally skipping a question. MCAR means that the probability of a missing value neither depends on any observed data, nor unobserved data. 10) and Rubin (1976) are missing completely at random (MCAR), missing at random (MAR), and not missing at random (NMAR). The three different missingness mechanisms as defined by Little and Rubin ( 2002, p. Three different missingness mechanisms can be distinguished (e.g., Little & Rubin, 2002 Van Buuren, 2012), which are discussed next.
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Whether or not results will be biased after listwise deletion is dependent on the underlying mechanism that caused the missing data, also known as the missingness mechanism. The second disadvantage is more serious: Results of statistical analyses may be biased. The first problem is wastefulness: It discards valuable information, which consequently leads to a loss of power.
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In several statistical software packages, such as SPSS 25.0 (SPSS, Inc., 2017), the most widely applied analyses use listwise deletion by default.Īlthough easy to apply, listwise deletion has two important disadvantages. The easiest way is to use listwise deletion, which excludes all respondents with missing data from the statistical analyses. Once confronted with missing data the question is how they can be handled. Missing data are a common problem in psychological research and many other scientific areas (see studies by Van Ginkel, Sijtsma, Van der Ark, & Vermunt, 2010, in the field of psychology Eekhout, de Boer, De Vet, & Heymans, 2012, in the field of epidemiology and Rombach, Rivero-Arias, Gray, Jenkinson, & Burke, 2016, in the field of quality of life research).
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