What’s missing completely at random data

Here are some more examples of MCAR (recall that Missing completely at random (MCAR) data occurs when the probability of missing data on a variable is independent of any other measured variables and the underlying values of the variable itself. ):

1. Survey Dropout: In a survey, if some participants do not answer a particular question purely by chance, and this non-response is not related to their characteristics or their responses to other questions, the missing data can be considered MCAR.
2. Lab Sample Errors: In a scientific experiment, if a certain percentage of lab samples are lost or destroyed due to random accidents (e.g., a technician accidentally drops some test tubes), and the loss of these samples is unrelated to the study variables, the missing data are MCAR.
3. Data Entry Mistakes: In a large database, if some data points are missing because of random typing errors or random technical glitches (e.g., power outages), and these mistakes are not related to the values of the data or other variables, the missing data can be classified as MCAR.
4. Mail Survey Responses: For a mailed survey, if some participants do not return the survey due to random reasons like misplacement of the survey forms or forgetting to mail them back, and this is unrelated to their demographics or opinions, the missing data are MCAR.
5. Random Absence in Class: In an educational study, if some students are absent on the day of a test due to random illnesses or personal reasons that do not correlate with their academic performance or other variables, the missing test scores are considered MCAR.

These examples highlight situations where the missing data occur purely by chance, without any systematic relationship with the observed or unobserved data.