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Related Concept Videos

Unusual Results01:16

Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Margin of Error01:27

Margin of Error

The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
Expected Value01:15

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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Related Experiment Video

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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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Published on: September 19, 2012

Rounding Probabilistic Expectations in Surveys.

Charles F Manski1, Francesca Molinari

  • 1Department of Economics and Institute for Policy Research, Northwestern University.

Journal of Business & Economic Statistics : a Publication of the American Statistical Association
|April 7, 2010
PubMed
Summary

Researchers often round numerical survey responses, impacting data analysis. This study infers rounding practices from response patterns, treating data as intervals to understand consequences and improve survey methods.

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Area of Science:

  • Survey methodology
  • Statistical analysis
  • Behavioral economics

Background:

  • Numerical survey responses are often rounded, introducing uncertainty.
  • Current analysis typically treats these rounded values as exact, ignoring potential bias.
  • Understanding and accounting for rounding is crucial for accurate empirical research.

Purpose of the Study:

  • To investigate the prevalence and extent of rounding in survey responses.
  • To develop a method for inferring individual rounding practices from response patterns.
  • To analyze the impact of rounding on empirical research and propose solutions.

Main Methods:

  • Analysis of response patterns from the Health and Retirement Study.
  • Statistical modeling to infer individual rounding behavior.
  • Application of interval data analysis techniques.

Main Results:

  • Strong evidence of systematic rounding in survey responses was found.
  • The extent of rounding varied significantly across respondents.
  • A novel method was developed to infer rounding practices from response patterns.

Conclusions:

  • Reported numerical survey responses should be interpreted as interval data.
  • Survey enrichment through probing questions can reveal rounding extent and reasons.
  • Accounting for rounding is essential for robust analysis of survey data.