The Risk of Disclosure When Reporting Commonly Used Univariate Statistics

Abstract

When basic or descriptive summary statistics are reported, it may be possible that the entire sample of observations is inadvertently disclosed, or that members within a sample will be able to work out responses of others. Three sets of univariate summary statistics that are frequently reported are considered: the mean and standard deviation; the median and lower and upper quartiles; the median and minimum and maximum. The methodology assesses how often the full sample of results can be reverse engineered given the summary statistics. The R package uwedragon is recommended for users to assess this risk for a given data set, prior to reporting the mean and standard deviation. It is shown that the disclosure risk is particularly high for small sample sizes on a highly discrete scale. This risk is reduced when alternatives to the mean and standard deviation are reported. An example is given to invoke discussion on appropriate reporting of summary statistics, also giving attention to the box and whiskers plot which is frequently used to visualise some of the summary statistics. Six variations of the box and whiskers plot are discussed, to illustrate disclosure issues that may arise. It is concluded that the safest summary statistics to report is a three-number summary of median, and lower and upper quartiles, which can be graphically displayed by the literal ‘boxplot’ with no whiskers.