Appendix A |
Errors and Uncertainties |
a) Absolute Difference
Comparisons can be made by taking the absolute difference (eg. my value is \(10~joules\) less than the accepted value). In this case either your value or the value compared needs to be stated for the difference to be put into context (An expected value of \(100,000~joules\) would mean the my value was quite good. Similarly an expected value of \(20~joules\) would say the opposite)
b) Percentage Difference
The percentage difference expresses the difference between two values as a percentage (eg. the difference was \(10\%)\). For this to be an accurate value one must also state from which value the percent was taken.
For example; to compare the number of students in a morning class of \(30~students\) with an evening class of \(25~students\) there is two possible ways of using percent difference (both correct). Which way the calculation is made becomes evident from how a statement is written with percent difference.
\[\text{percent difference}=\left ( \frac{30 - 25}{30\text{ in the morning}}\right )\times100\%=17\%\] | The evening class has \(17\%\) less students than the morning class. |
\[\text{percent difference}=\left ( \frac{30 - 25}{25\text{ in the evening}}\right )\times100\%=20\%\] | The morning class has \(20\%\) more students than the evening class. |
A simple approach to remembering how to correctly write a statement using percent difference is to realize the value quoted at the end of the statement is the target value (the one divided by).
30 fish difference |
43 fish difference |
The original number of fish is \(30\%\) more than the 100 returning fish. | The returning 100 fish is \(30\%\) less than the original number of fish. |
(\((130-100)/100)\times100\% = 30\%\) |
(\((143-100)/143)\times100\% = 30\%\) |
Note that percent difference is calculated without uncertainties. The difference, as either an absolute or a percent, is often used to compared with the uncertainties in the values in considering the agreement of the values.