Related Experiment Video
Updated: Aug 9, 2026
04:40
Tactile Semiautomatic Passive-Finger Angle Stimulator (TSPAS)
Published on: July 30, 2020
A robust confidence interval for location for symmetric, long-tailed distributions
1Department of Statistics, Princeton University, Princeton, New Jersey 08540.
Summary
The new wave-interval procedure provides a robust 95% confidence interval for symmetric distributions. It is efficient for normal data and reliable for long-tailed distributions, reducing the risk of understating findings.
Area of Science:
- Statistics
- Statistical Inference
Background:
- Traditional confidence intervals may lack efficiency with non-normal data.
- Long-tailed distributions pose challenges for standard statistical methods.
Purpose of the Study:
- Introduce the wave-interval procedure for calculating 95% confidence intervals.
- Evaluate its performance across various symmetric distributions, including normal and long-tailed ones.
Main Methods:
- The wave-interval procedure is a novel statistical method.
- It utilizes readily available t-tables for calculations.
Main Results:
- The wave-interval demonstrates high efficiency with normally distributed data.
- It maintains good performance even with data from long-tailed distributions like the Cauchy distribution.
- The procedure minimizes the risk of drawing unsupported conclusions.
Conclusions:
- The wave-interval is a recommended procedure for sample sizes of eight or more.
- It offers a reliable and efficient method for estimating the center of symmetric distributions.
Related Concept Videos
00:54Uncertainty: Confidence Intervals
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
01:31Student t Distribution
The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the population standard deviation using a confidence interval, which provides results close enough to the original value. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
The Student t distribution was developed by William S. Goset (1876–1937) of the...
The Student t distribution was developed by William S. Goset (1876–1937) of the...
01:21Confidence Intervals
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
A confidence...
01:25Confidence Interval for Estimating Population Mean
A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
01:19Interpretation of Confidence Intervals
A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
01:22Estimating Population Mean with Unknown Standard Deviation
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
William S. Gosset (1876–1937) of the Guinness...