Why Does Subtractive Cancellation Affect Measurement Precision?

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In summary, when subtracting measurements with similar values, there is a potential for significant levels of error due to subtractive cancellation or significance loss. This issue is known as the propagation of errors or uncertainty, and it is not specific to experimental measurements. The size of the estimate plays a role in the relative uncertainty, making it larger when subtracting rather than adding.
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Roger Dodger
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When subtracting measurements that each have a certain level of uncertainty, we can end up with huge levels of error if the two measurements are roughly equal in value. However, this problem doesn't appear when adding numbers.

Question: Is there a name for this type of error? Does anyone discuss the problems associated with subtracting measurements that are similar in magnitude? I can't seem to find anything on this source of error, possibly because I don't know what it's called.

In numerical analysis, they call this subtractive cancellation or significance loss and the uncertainty in the numbers is due to the truncation of numbers to fit in a computer's memory. But I cannot find anything on this effect for experimental measurements.
 
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It is usually called the propagation of errors or propagation of uncertainty. The uncertainty is not larger from subtracting rather than adding. The difference is the size of the estimate. This makes the relative uncertainty larger because the relative uncertainty is the uncertainty divided by the estimate.
 
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Related to Why Does Subtractive Cancellation Affect Measurement Precision?

1. What are subtractive errors in the lab?

Subtractive errors in the lab refer to mistakes or inaccuracies that occur during the process of subtracting values or measurements in an experiment. These errors can lead to incorrect data and affect the overall accuracy of the results.

2. What causes subtractive errors in the lab?

Subtractive errors can be caused by a variety of factors, such as human error, faulty equipment, or incorrect calculations. They can also occur due to environmental factors, such as temperature or humidity, which can affect the accuracy of measurements.

3. How can subtractive errors be minimized in the lab?

To minimize subtractive errors in the lab, it is important to carefully follow experimental procedures and double-check all calculations. Regularly calibrating and maintaining equipment can also help reduce errors. Additionally, having multiple trials and replicates can help identify and account for any discrepancies in data.

4. What are the potential consequences of subtractive errors in the lab?

If subtractive errors are not identified and corrected, they can lead to inaccurate data and ultimately affect the validity of the experiment's results. This can have serious consequences, especially in scientific research where accurate data is crucial.

5. How can subtractive errors be detected and corrected?

To detect and correct subtractive errors, it is important to carefully review all data and calculations, and compare them to expected results. If any discrepancies are found, the experiment should be repeated or adjustments should be made to the procedures or equipment. It is also helpful to have a colleague or supervisor review the data to catch any errors that may have been missed.

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