How is uncertainty affected by absolute numbers?

In summary, there are different ways to calculate the uncertainty for the evaporation rate of water. One approach is to use Gaussian error propagation for rates within 30 seconds, but for the average rate, it is better to use the first and last measurements or do a least squares fit to a regression line. While there are ways to calculate the uncertainty using the propagation of errors formula, it may not be the best approach. Additionally, it is important to consider the dependency of the evaporation rate on the total amount of water present at a given time.
  • #1
legends784
Example:
Say I want to calculate the evaporation rate of water and so I record the mass of some amount of water every 30 seconds for 5 minutes. The uncertainty in the scale is inherently .0001g and so that would be the uncertainty in the mass of any individual measurement, but how would I calculate the uncertainty for what I am actually looking for which is a rate. I.e by finding the difference between each concurrent measurement, dividing it by 30seconds, then adding up each of the individual rates in g/s and calculating an average rate in mg/min.

I can't physically wrap my head around how the error transfers between each of these stages, especially because most of them involve dividing/multiplying by absolute numbers like 30seconds or 1000mg/g

All help is appreciated,
Alex
 
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  • #2
If you divide or multiply by constants the relative uncertainty stays the same. For evaporation rates within 30 seconds Gaussian error propagation will work.
For the average, this doesn't work, as your measurements are correlated: If a measurement (apart from the first and last one) is off, it will increase one rate and decrease another. It won't influence the average at all.

You can calculate the average and its uncertainty just from the first and last measurement, similar to the 30s values. You'll get a better estimate if you make a trend line through all your data, however.
 
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  • #3
legends784 said:
what I am actually looking for which is a rate. I.e by finding the difference between each concurrent measurement, dividing it by 30seconds, then adding up each of the individual rates in g/s and calculating an average rate in mg/min.
A better approach would be to do a least squares fit to a regression line and obtain the slope. Most commercial packages will give you a standard error or a confidence interval for the slope.

There are ways to calculate what you suggest using the propagation of errors formula, but I would not recommend that approach.
 
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  • #4
Doesn't the amount that evaporates at stage ##t_0## also depend on the total amount of water present at ##t_0##?
 

1. How is uncertainty measured?

Uncertainty is typically measured using statistical methods such as standard deviation, variance, or confidence intervals. These methods help quantify the amount of variation or error in a set of data.

2. Can absolute numbers have uncertainty?

Yes, absolute numbers can have uncertainty. For example, if a measurement is made using a ruler with markings only to the nearest centimeter, the measurement will have an uncertainty of +/- 0.5 cm.

3. How does the size of the absolute number affect uncertainty?

The size of the absolute number does not necessarily affect uncertainty. However, larger absolute numbers may have a smaller relative uncertainty compared to smaller absolute numbers. For example, a measurement of 100 cm with an uncertainty of 1 cm has a relatively smaller uncertainty compared to a measurement of 1 cm with an uncertainty of 1 cm.

4. Is uncertainty affected by the precision of the measurement instrument?

Yes, the precision of the measurement instrument can affect uncertainty. The more precise the instrument, the smaller the uncertainty will be. However, even with a very precise instrument, there will always be some level of uncertainty in a measurement.

5. How does uncertainty impact the validity of scientific findings?

Uncertainty is an important factor to consider in scientific findings, as it reflects the reliability and accuracy of the data. High levels of uncertainty can affect the validity of results and may require further investigation or replication of the study. Scientists must carefully consider and report uncertainty in their findings to ensure the credibility of their research.

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