Effects of Grouping Data on First and Second Distribution Moments

• Activity Number: 229
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Myron Katzoff*+ and Jay J. Kim and Joe Fred Gonzalez, Jr. and Lawrence H. Cox
• Companies: National Center for Health Statistics and National Center for Health Statistics and Centers for Disease Control and Prevention and National Center for Health Statistics
• Keywords: disclosure risk ; interval-data ; variance ; class mark ; data summarization ; midpoint

Abstract

Data such as income are often grouped and released as interval data, considered to be one of the best ways of summarizing data which has disclosure risk implications as well. Class marks (midpoints) of intervals are then used to calculate the mean and variance of the grouped data. In most situations, using midpoints for every observation in the interval smoothes the data, thereby reducing the variance. It can be shown, as in analysis of variance, that, using midpoints, we lose the within-interval variance component if within-interval data have a uniform distribution. However, if distributions within some intervals are peaked or skewed, use of the midpoints of the interval data can result in higher variance estimates than would be obtained with the raw data. Moreover, for those data, the mean of the grouped data based on the use of midpoints is biased. If class (conditional) means are used for calculating overall mean and variance, the mean of the raw data can be recaptured and the variance will be lower. We report some initial results from our study of the impact of accepted practices for approximating moments with summarized data.