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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.

Random and Systematic Errors

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

Systematic Error: Methodological and Sampling Errors

Systematic Error: Methodological and Sampling Errors

In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

Wald-Wolfowitz Runs Test II

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...

Random and Systematic Errors

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

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Related Experiment Video

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Uniform-penalty inversion of multiexponential decay data. II. Data spacing, T(2) data, systemic data errors, and

G C Borgia¹, R J Brown, P Fantazzini

¹Department of ICMA, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)

|December 1, 2000

Summary

Uniform Penalty Inversion (UPEN) is extended for T(2) relaxation data, improving analysis of complex decay curves. This method enhances resolution and identifies data issues, crucial for accurate relaxation time distribution analysis.

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Area of Science:

Nuclear Magnetic Resonance Spectroscopy
Data Analysis and Signal Processing

Background:

The Uniform Penalty Inversion (UPEN) method was previously established for T(1) relaxation data analysis.
UPEN utilizes negative feedback in regularization to optimize smoothing based on feature sharpness.
Previous applications focused on data with uniform log-time spacing.

Purpose of the Study:

To extend the UPEN method for analyzing T(2) relaxation data, which often has linear time spacing.
To incorporate data window averaging and weighting factors into the UPEN computation.
To develop diagnostic tools for identifying systematic errors and improving data quality in relaxation analysis.

Main Methods:

Extension of UPEN algorithm to accommodate T(2) data with arbitrary spacing.
Implementation of data window averaging and associated weighting.
Development and application of diagnostic parameters to detect instrumental and data acquisition issues.
Evaluation of the reduced need for non-negativity constraints.

Main Results:

UPEN successfully applied to T(2) relaxation data with varying spacings.
Averaging and weighting strategies enhance the analysis of T(2) decay curves.
Diagnostic parameters effectively identify systematic errors, such as artificial curve narrowing.
Meaningful resolution of closely spaced peaks in relaxation time distributions is improved.

Conclusions:

The extended UPEN method provides robust analysis for T(2) relaxation data.
Diagnostic tools are vital for ensuring data integrity and accurate interpretation of relaxation time distributions.
Near real-time processing with UPEN can facilitate timely instrument adjustments and data correction.