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When should I select pairwise deletion?

So I grasp the idea of pairwise deletion, but what conditions are actually needed to select this? Is it when data is MCAR? Why would researches select this method? I am carrying out a study with 200 participants working on the assumption that data is MCAR but In my research I want to justify the reasons to choose pairwise.

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First and foremost, you need to determine the mechanism through which your data is missing. It appears from your post that you are assuming that your data is MCAR - which would mean that listwise/pairwise deletion are appropriate approaches to addressing your missing data.

However, it is important to accurately determine the mechanism of your missing data as it may also be missing at random (MAR) - in which case Multiple Imputation or Maximum Likelihood is the more appropriate route to take. The most difficult scenario would be if your data is missing not at random (MNAR).

Generally speaking, MCAR is usually unrealistic, MAR is somewhat plausible, while MNAR is often plausible. As such, MCAR and MAR are typically considered "ignorable" as information about the missing data itself is not included when dealing with the missing data. In contrast, MNAR is typically "non-ignorable" because the missing data mechanism must be modelled while you deal with the missing data.

When using the listwise deletion approach, a case is dropped from an analysis because it has a missing value in at least one of the specified variables. The analysis is only run on cases which have a complete set of data. For example, say you are conducting analysis using reaction time, hours of training, body weight, and height. Participant X is missing data for reaction time; thus, participant X will be completely removed from the analyses because they do not have complete data for all of the four variables listed.

In contrast, when using the pairwise approach, deletion occurs when the statistical procedure uses cases that contain some missing data. The procedure cannot include a particular variable when it has a missing value, but it can still use the case when analyzing other variables with non-missing values. As such, pairwise deletion retains more data (i.e., participants) wherever possible. Again, for the example listed in the previous paragraph, Participant X will only be omitted from analyses using reaction time, but not be omitted from analyses for which they have complete data (i.e., hours of training, body weight, and height).

Both listwise and pairwise deletion methods make very strict assumptions about the mechanisms that cause data to be missing. In order for these methods to produce appropriate results in most situations, data must be MCAR. Without data that is MCAR, using listwise/pairwise deletion methods may produce bias parameters and estimates not representative of the actual data.

Source: https://www.ibm.com/support/pages/pairwise-vs-listwise-deletion-what-are-they-and-when-should-i-use-them

Recent research by Woods et al. (in press) recommends using multiple imputation (MI) rather than listwise/pairwise deletion techniques, as the latter results in potential loss of statistical power, constraints of generalizability, and the extremely high likelihood that the MCAR assumption is not met. (Source: https://psyarxiv.com/uaezh)

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