Standard Deviation or Resolution Error: Which One Should Be Quoted in a Report?

[Max Eilerson]

In a report should I be quoting uncertainties as 2.435(36) m or
2.435 +- 0.036 m. It seems the first way is usually used when quoting a standard deviation error and the second when quoting a resolution error.

 

[Ertosthnes]

That makes sense to me. So, in the report, is the error due to standard deviation (from a sample of data) or is it due to the resolution of the equipment?

 

[m2003]

As a scientist, it is important to accurately represent the uncertainties in your measurements in order to ensure the validity and reliability of your findings. Both standard deviation and resolution error are commonly used to indicate the level of uncertainty in a measurement, but they represent different sources of error and should be used in different contexts.

Standard deviation is a measure of the spread of data around the mean value, and is typically used when reporting the variability or precision of a measurement. On the other hand, resolution error refers to the smallest increment that can be measured with a given instrument, and is used to indicate the accuracy or sensitivity of a measurement.

In the case of your example, the first format (2.435(36) m) indicates that the measurement has a mean value of 2.435 m with a standard deviation of 0.036 m. This means that the actual value could be anywhere within 0.036 m above or below the reported value. This format is commonly used when reporting the precision of a measurement, as it gives an indication of the range of values that can be expected from repeated measurements.

The second format (2.435 ± 0.036 m) indicates that the measurement has a mean value of 2.435 m with a resolution error of 0.036 m. This means that the actual value could differ from the reported value by up to 0.036 m due to limitations in the measuring instrument. This format is typically used when reporting the accuracy of a measurement, as it gives an indication of the potential error introduced by the instrument itself.

In conclusion, the choice between reporting standard deviation or resolution error depends on the purpose of your report and the type of uncertainty you want to convey. It is important to use the appropriate format in order to accurately communicate the level of uncertainty in your measurements.