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Rules for Significant Figures

Rules for Significant Figures

In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise.
It should be emphasized that when we represent measured values, the...

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 in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

Accuracy and Precision

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. Highly accurate...

Accuracy and Precision

Accuracy and Precision

Uncertainty in Measurement: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

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Related Experiment Video

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Precision of In Vivo Quantitative Tooth Wear Measurement Using Intra-Oral Scans

Precision of In Vivo Quantitative Tooth Wear Measurement Using Intra-Oral Scans

Published on: July 12, 2022

Validating precision--how many measurements do we need?

Arne ÅSberg¹, Kristine Bodal Solem, Gustav Mikkelsen

¹Department of Clinical Chemistry, Trondheim University Hospital , Trondheim , Norway.

Scandinavian Journal of Clinical and Laboratory Investigation

|June 18, 2015

Summary

To ensure analytical method precision, the entire 90% confidence interval for the true standard deviation must be below acceptable limits. Power function curves aid in determining the necessary number of measurements for validation.

Keywords:

Chemistry techniques analytical/methods imprecision precision quality control sample size

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Area of Science:

Analytical Chemistry
Method Validation
Statistical Analysis

Background:

Ensuring sufficient precision in quantitative analytical methods is crucial.
Current standards require imprecision (standard deviation) to be below an acceptable threshold.
A more rigorous approach proposes the entire 90% confidence interval for true standard deviation must lie below this threshold.

Purpose of the Study:

To propose a statistically robust criterion for validating analytical method precision.
To introduce power function curves for determining optimal sample sizes in precision studies.

Main Methods:

Computer simulations were employed to calculate the probability of exceeding acceptable standard deviation limits.
Power function curves were generated for various experimental scenarios.

Main Results:

The probability of failing to assure precision increases with fewer measurements and higher standard deviations.
With true standard deviation at 80% of acceptable, 40 measurements yield a 42% failure rate, while 100 measurements reduce it to 7%.
The proposed method is more reliable than CLSI guidelines but requires more measurements.

Conclusions:

Power function curves are valuable tools for planning precision validation studies.
This approach enhances the reliability of analytical method precision validation.