Abstract: Entropy quantifies uncertainty in a data set. Intuition tells us that missing values should increase the uncertainty in a data set, but the affect of missing values on entropy has never been quantified. This paper develops formulae for the entropy of incomplete normal data under different missingness mechanisms. The results are compared to the fraction of missing information, which quantifies uncertainty in parameter estimates due to missing values, to compare the two measurements of uncertainty.

Key words and phrases: Entropy, fraction of missing information, missing data, multiple imputation.