insikt - Statistics - # Confidence Intervals for Percentiles

Understanding Confidence and Assurance in Percentiles

Q: What are the implications of expanding tolerance intervals as percentile or confidence levels increase

Expanding tolerance intervals as percentile or confidence levels increase has significant implications on data interpretation and decision-making processes. As these intervals widen with higher percentiles at a constant level of confidence or vice versa – increasing confidences at fixed percentiles – it indicates greater uncertainty in estimating where a certain fraction of population samples lie within a given range. This expansion implies that as more extreme values (higher percentiles) are considered or when higher levels of certainty (increased confidences) are required in defining these ranges, there is a trade-off with broader intervals which encompass more data points. Consequently, this widening could impact risk assessments based on these tolerance limits and influence strategies related to quality control measures or process improvements depending on how much variation can be tolerated within specified bounds.

Q: How can the concept of assurance from reliability engineering be applied in other statistical contexts

The concept of assurance from reliability engineering can be applied effectively in various statistical contexts beyond just tolerance interval calculations. By extending assurance principles to statistical analyses involving parameters like means, medians, quantiles etc., researchers can communicate not only their findings but also convey an additional layer of reliability associated with those results. For instance: Parameter Estimation: Calculating assurance levels alongside point estimates provides stakeholders with information regarding how confident they should be in those estimations. Hypothesis Testing: Incorporating assurance metrics into hypothesis testing procedures offers a clearer understanding of result significance while considering potential uncertainties. Predictive Modeling: Utilizing assurance concepts when developing predictive models allows for conveying not only accuracy but also reliability expectations associated with model predictions. By integrating assurance considerations into diverse statistical applications, practitioners enhance transparency and trustworthiness in their analytical outcomes while offering stakeholders valuable insights into result dependability under varying conditions.

Centrala begrepp

The author explores the concept of confidence intervals for percentiles, comparing them to mean intervals and introducing the idea of assurance intervals based on reliability engineering.

Sammanfattning

The article delves into deriving expressions for confidence in percentiles, contrasting it with mean intervals. It introduces assurance intervals aligning with confidence levels and provides a numerical method for computation. The relationship between confidence intervals of median and mean is explored across different distributions, showcasing how they vary with sample sizes. Additionally, the discussion extends to tolerance intervals and the concept of assurance from reliability engineering.

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arxiv.org

Statistik

"95% confidence interval range is 0.14 for median and 0.12 for mean."
"For one example full set of 1000 samples, the 95% confidence interval range is 0.14 for median and 0.12 for mean."
"Experiment repeated 100 times to generate pairs of 95% confidence interval values for mean and median."
"Tolerance interval expands as percentile level increases at constant confidence level."
"Tolerance interval expands as confidence level increases at constant percentile level."

Citat

"The concept of assurance was introduced in reliability engineering by Fulton by simply setting reliability equal to confidence."
"Assurance intervals match percentiles with confidence and are easier for communication."

Viktiga insikter från

Confidence and Assurance of Percentiles

by Sanjay M. Jo... på arxiv.org 03-01-2024

https://arxiv.org/pdf/2402.19109.pdf

Djupare frågor

How does the relationship between confidence intervals of median and mean impact statistical analysis

The relationship between confidence intervals of median and mean plays a crucial role in statistical analysis. When comparing the confidence intervals of the median and mean for different distributions, such as normal, uniform, or exponential, insights into the symmetry or asymmetry of the data distribution can be gained. In cases where the distribution is symmetrical, like in normal and uniform distributions, if the mean and median are expected to be similar but have differing confidence intervals, it could indicate underlying issues with sample size or variability within the dataset. On the other hand, for asymmetrical distributions like exponential distribution where the median is typically smaller than the mean due to skewness towards lower values, observing comparable confidence intervals for both statistics may suggest specific characteristics about that dataset's shape.

What are the implications of expanding tolerance intervals as percentile or confidence levels increase

Expanding tolerance intervals as percentile or confidence levels increase has significant implications on data interpretation and decision-making processes. As these intervals widen with higher percentiles at a constant level of confidence or vice versa – increasing confidences at fixed percentiles – it indicates greater uncertainty in estimating where a certain fraction of population samples lie within a given range. This expansion implies that as more extreme values (higher percentiles) are considered or when higher levels of certainty (increased confidences) are required in defining these ranges, there is a trade-off with broader intervals which encompass more data points. Consequently, this widening could impact risk assessments based on these tolerance limits and influence strategies related to quality control measures or process improvements depending on how much variation can be tolerated within specified bounds.

How can the concept of assurance from reliability engineering be applied in other statistical contexts

The concept of assurance from reliability engineering can be applied effectively in various statistical contexts beyond just tolerance interval calculations. By extending assurance principles to statistical analyses involving parameters like means, medians, quantiles etc., researchers can communicate not only their findings but also convey an additional layer of reliability associated with those results. For instance:

Parameter Estimation: Calculating assurance levels alongside point estimates provides stakeholders with information regarding how confident they should be in those estimations.
Hypothesis Testing: Incorporating assurance metrics into hypothesis testing procedures offers a clearer understanding of result significance while considering potential uncertainties.
Predictive Modeling: Utilizing assurance concepts when developing predictive models allows for conveying not only accuracy but also reliability expectations associated with model predictions.
By integrating assurance considerations into diverse statistical applications, practitioners enhance transparency and trustworthiness in their analytical outcomes while offering stakeholders valuable insights into result dependability under varying conditions.