Extent Of Rounding Research Articles

Uncertainty causes rounding: an experimental study

Rounding is a common phenomenon when subjects provide an answer to an open-ended question, both in experimental tasks and in survey responses. From a statistical perspective, rounding implies that the measured variable is a coarsened version of the underlying continuous target variable. Since the coarsening process is non-random, inference from rounded data is generally biased. Despite the potentially severe consequences of rounding, little is known about its causes. In this paper, we focus on subjects' uncertainty about the target variable as one potential cause for rounding behavior. We present a novel experimental method that induces uncertainty in a controlled way, thus providing causal evidence for the effect of subjects' uncertainty on the extent of rounding. Then, we specify and estimate a mixture model that relates uncertainty and rounding. The results suggest that an increase in the exogenous level of uncertainty translates into higher variance of the subjects' beliefs, which in turn results in more rounding.

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.

Can Subjective Expectations Data be Used in Choice Models? Evidence on Cognitive Biases

A pervasive concern with the use of subjective data in choice models is that the data are biased and endogenous. This paper examines the extent to which cognitive biases plague subjective data, specifically addressing 1) whether cognitive dissonance affects the reporting of beliefs, and 2) whether individuals exert sufficient mental effort when probed about their subjective beliefs. For this purpose, I collect a unique panel data set of Northwestern University undergraduates that contains their subjective expectations about outcomes specific to different majors in their choice set. I do not find evidence of cognitive biases systematically affecting the reporting of beliefs: By analyzing patterns of belief updating, I can rule out cognitive dissonance being a serious concern in the current setting. Moreover, there seems to be no systematic (nonclassical) measurement error in the reporting of beliefs. In the reported beliefs for the various majors, I find no systematic patterns in mental recall of previous responses or in the extent of rounding. Comparison of subjective beliefs with objective measures suggests that students have well-formed expectations. Overall, the results paint a favorable picture for the use of subjective expectations data in choice models.

The effects of high hydrostatic pressure on human cells in primary and continuous culture

Observations have been made on the effect of high hydrostatic pressure on human amnion cells in primary culture and a variety of human cells in continuous culture. All cell lines round up under pressure and the extent of rounding is directly proportional to the amount of pressure applied. A reduction in temperature allows a proportionate reduction in pressure for the achievement of the same morphologic end-point. Upon application of pressure, cells of continuous lines undergo a pronounced surface bleb activity which soon recedes as the cells round up. Following release of pressure, there is a marked contraction of these cells and subsequent resumption of bleb activity. Primary amnion cells exhibit neither contraction nor bleb activity. All the pressure effects are completely reversible. The entire sequence of events is discussed in relation to cytoplasmic sol-gel transformations and the potential contractility of the gel.