Difference between revisions of "Fifteen-unit rule for rounding numerical results"
From Testiwiki
(created) |
m |
||
| Line 8: | Line 8: | ||
==Definition== | ==Definition== | ||
| − | Usually, from scientific studies (whether based on physical measurements or mathematical modelling), numerical results are obtained that consist of | + | Usually, from scientific studies (whether based on physical measurements or mathematical modelling), numerical results are obtained that consist of an average value or a best estimate (e.g. 4.5678 meters) and a measure of the probable uncertainty (e.g. ±0.2345 meters). However, as raw figures, either or both of these may be too precise (i.e. contain more digits than is justifiable or meaningful). |
| − | + | Thus, before publishing, a systematic method for rounding those results to a justifiable and meaningful precision is needed, in order to avoid a misconception of excessively (in)accurate results. | |
==Result== | ==Result== | ||
| Line 24: | Line 24: | ||
Please see the following examples: | Please see the following examples: | ||
| − | * | + | * <font color=red>(1062 ± 41) meters</font> is '''incorrect''', because the LSD of the average value (2) is associated with an uncertainty of 41 units (and the uncertainty is expressed using a precision of 41 units) |
| − | * | + | * <font color=green>(1060 ± 50) meters</font> is '''correct''', because the LSD of the average value (6) is now associated with an uncertainty of 5 units only (and the uncertainty is expressed using a precision of 5 units) |
:: - Note that the original uncertainty (41) has been rounded upwards (to 50). | :: - Note that the original uncertainty (41) has been rounded upwards (to 50). | ||
| − | * | + | * <font color=red>(0.8765 ± 0.0132) kg</font> is '''incorrect''', because the LSD of the average value (5) is associated with an uncertainty of 132 units (and the uncertainty is expressed using a precision of 132 units) |
| − | * | + | * <font color=green>(0.876 ± 0.014) kg</font> is '''correct''', because the LSD of the average value (6) is now associated with an uncertainty of 14 units only (and the uncertainty is expressed using a precision of 14 units) |
:: - Note that the original uncertainty (0.0132) has been rounded upwards (to 0.014). | :: - Note that the original uncertainty (0.0132) has been rounded upwards (to 0.014). | ||
Revision as of 15:22, 8 August 2011
This page is a method.
The page identifier is Op_en5327 |
|---|
| Moderator:Erkki Kuusisto (see all) |
| This page is a stub. You may improve it into a full page, and then a rating bar will appear here. |
| Upload data
|
Scope
When presenting the final results of a study, what is the proper way of rounding numerical results of the form "average ± probable uncertainty"?
Definition
Usually, from scientific studies (whether based on physical measurements or mathematical modelling), numerical results are obtained that consist of an average value or a best estimate (e.g. 4.5678 meters) and a measure of the probable uncertainty (e.g. ±0.2345 meters). However, as raw figures, either or both of these may be too precise (i.e. contain more digits than is justifiable or meaningful).
Thus, before publishing, a systematic method for rounding those results to a justifiable and meaningful precision is needed, in order to avoid a misconception of excessively (in)accurate results.
Result
The 15-unit rule says that:
- in the average value, the uncertainty of the least significant digit (LSD) must not exceed 15 units,
- the probable uncertainty must not exceed 15 units (where one unit pertains to the LSD of the average value)
- the probable uncertainty is always rounded upwards.
Please see the following examples:
- (1062 ± 41) meters is incorrect, because the LSD of the average value (2) is associated with an uncertainty of 41 units (and the uncertainty is expressed using a precision of 41 units)
- (1060 ± 50) meters is correct, because the LSD of the average value (6) is now associated with an uncertainty of 5 units only (and the uncertainty is expressed using a precision of 5 units)
- - Note that the original uncertainty (41) has been rounded upwards (to 50).
- (0.8765 ± 0.0132) kg is incorrect, because the LSD of the average value (5) is associated with an uncertainty of 132 units (and the uncertainty is expressed using a precision of 132 units)
- (0.876 ± 0.014) kg is correct, because the LSD of the average value (6) is now associated with an uncertainty of 14 units only (and the uncertainty is expressed using a precision of 14 units)
- - Note that the original uncertainty (0.0132) has been rounded upwards (to 0.014).
