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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Friedman Two-way Analysis of Variance by Ranks

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

Uncertainty: Confidence Intervals

Uncertainty: 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...

Ranks

Ranks

Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...

Propagation of Uncertainty from Random Error

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 Videos

Uncertainty in Rank Estimation: Implications for Value-Added Modeling Accountability Systems.

J R Lockwood¹, Thomas A Louis, Daniel F McCaffrey

¹RAND.

Journal of Educational and Behavioral Statistics : a Quarterly Publication Sponsored by the American Educational Research Association and the American Statistical Association

|October 16, 2009

Summary

Estimating teacher and school quality using student test scores is complex. Even optimal ranking methods show large errors, questioning their use in educational accountability.

Related Experiment Videos

Area of Science:

Educational Measurement
Statistical Modeling
Psychometrics

Background:

Accountability in public education often relies on ranking teachers and schools by student test scores.
While methods for estimating teacher/school effects are known, rank estimator properties are less understood.

Purpose of the Study:

Investigate the performance of rank (percentile) estimators in hierarchical models.
Analyze the mean squared error (MSE) and operating characteristics of decision rules based on estimated percentiles.

Main Methods:

Utilized a basic, two-stage hierarchical model to simulate performance.
Studied MSE and decision rule characteristics influenced by signal-to-noise ratio and number of schools/teachers.

Main Results:

High MSE was observed for commonly encountered variance ratios, even with optimal procedures.
Performance depends on the signal-to-noise ratio, with moderate dependence on the number of schools/teachers.
Interactions between variance ratios and estimators were noted, particularly for extreme percentiles.

Conclusions:

Optimal percentile estimators may not perform sufficiently well for evaluating teachers or schools.
The statistical and practical complexity of value-added modeling necessitates careful assessment of percentile estimator utility.