Rounding Probabilistic Expectations in Surveys
研究受访者在回答未来事件发生概率时如何四舍五入，利用健康与退休调查数据发现普遍存在四舍五入且程度因人而异，提出通过回答模式推断四舍五入行为，将数值视为区间数据，并分析其对实证研究的影响。
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 paper 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, the extent of rounding differing across respondents. We propose use of a person's response pattern across different questions to infer his 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.