Error Analysis
The following techniques are used to determine how error propagates through an experimental procedure. This method is based upon combining the uncertainty for each step.
Calculations
Symbols used:
- x; result of calculation
- a, b & c; numbers used for calculation
- s_{x}; uncertainty in result
- s_{a}, s_{b} & s_{c}; uncertainty in numbers used for calculation
Operations
- Addition and Subtraction
x = a + b - c
- Multiplication and Division
x = a * b/c
- Exponentiation (assuming no uncertainty in b)
x = a^{b}
- Logarithm
- Base 10
x = log_{10} a
- Base e
x = ln a
- Antilog
- Base 10
x = 10^{a} a
- Base e
x = e^{a}
Example
- From a calibration curve the concentration of an unknown is 16±2 ppm.
- The solution was prepared by:
- dissolving 0.0452±0.0001 g of compound
- in 250.0±0.1 ml of water
- From this the weight of unknown in the compound is:
- x = 16 ppm * 250 ml * (mg/l) * (1 g/1000 mg) * (1 l/1000 ml)
- x = 0.0040 g of unknown in the compound
- The uncertainty in this weight is:
- Therefor the weight of the unknown is:
0.0040±0.0005 g (or 4.0±0.5 mg)