In the case of missing completely at random, the assumption was that there was no pattern. It is only likely to be true in situations where the data is missing due to some truly random phenomena (e.g., if people were randomly asked 10 of 15 questions in a questionnaire). The MCAR assumption is rarely a good assumption. When data is missing completely at random, it means that we can undertake analyses using only observations that have complete data (provided we have enough of such observations). A more formal way of testing is to use Little’s MCAR test. If you can predict which units have missing data (e.g., using common sense, regression, or some other method), then the data is not MCAR. It is relatively easy to check the assumption that data is missing completely at random. This is known as assuming that the missing value is m issing completely at random (MCAR). When we make this assumption, we are assuming that whether or not the person has missing data is completely unrelated to the other information in the data. We could assume, therefore, that there is a 50% chance she has a high income and a 50% chance she has a low income. Looking at the table below, we need to ask ourselves: what is the likely income of the fourth observation? The simplest approach is to note that 50% of the other people have high incomes and 50% have low incomes. How many colas did you drink in the past 24 hours? IDĭid you drink Coca-Cola in the last 24 hours? In this case, we can logically deduce that the correct value is 0, so this value should be used in place of the missing values in our analysis. In the How many colas did you drink in the past 24 hours column, there are also structurally missing values. This situation is typically best addressed by excluding people with such missing data from any analysis of the variables with the structurally missing values. In the table below, the first and third observations have missing values for Age of youngest child. This is because these people have no children. In other words, it is data that is missing because it should not exist. Structurally missing data is data that is missing for a logical reason. Different types of missing data need to be treated differently in order for any analysis to be meaningful. Missing data is either: structurally missing, missing completely at random (MCAR), missing at random, or nonignorable (also known as missing not at random). There are four qualitatively distinct types of missing data.
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