Rounding probabilistic expectations in surveys

Rounding is the familiar practice of reporting one value whenever a real number lies in an interval. Uncertainty about the extent of rounding is common when researchers analyze survey responses to numerical questions. The prevalent practice has been to take numerical responses at face value, even though many may in fact be rounded. This article studies the rounding of responses to survey questions that ask persons to state the percent chance that some future event will occur. We analyze data from the Health and Retirement Study and find strong evidence of rounding, with the extent of rounding differing across respondents. We propose use of a person's response pattern across different questions to infer the person's rounding practice, the result being interpretation of reported numerical values as interval data. We then bring to bear recent developments on statistical analysis of interval data to characterize the potential consequences of rounding for empirical research. Finally, we propose enrichment of surveys by probing to learn the extent and reasons for rounding.