Error Analysis Example
Error analysis is always a difficult area for students. However, the careful consideration of
experimental error is one of the important skills that we need to learn to be effective scientists. In
the following discussion, the errors in a titration experiment are considered. The first section is a
detailed look at how to determine the most important errors. The second section is an example of
the corresponding text that would be written in a lab report for CH141-142.
Determining the Important Errors
The purpose of the error analysis section of the lab report is to determine the most important
errors and the effect that those errors have on the final result.
Random Errors: Random errors cause positive and negative deviations from the average
value of a measurement. Random errors cancel by averaging, if the experiment is repeated many
times. Upon averaging many trials, random errors have an effect only on the precision of a
measurement. The effect of random errors is primarily on the precision. Every non-integer
experimental measurement is a source of random error. The random error is estimated from the
readability of the device. A table of typical measurements and the associated precision, under
practical circumstances, is given below. For instrument readings, to avoid round-off error, report
one extra significant figure and then underline the digit that is not significant.
Volumetric flasks and pipettes precision (relative) significant figures
10 mL
0.03 mL 3 i.e. 10.0 mL
25 mL
0.03 mL 3 25.0 mL
50 mL
0.05 mL 3 50.0 mL
100 mL
0.08 mL 4 100.0 mL
Auto-pipettors
10
L
0.05
L (0.5%) 3 i.e. 10.0
L
100
L
0.3
L (0.3%) 3 100.
L
1000
L
2
L (0.2%) 3 1000.
L
Analytical Balance
0.1000 g
0.0001 g 4 e.g. 0.3456 g
1.0000 g
0.0001 g 5 2.3456 g
10.0000 g
0.0001 g 6 12.3456 g
Spectrophotometer (Spectro-Viz
*
)
0.100
0.003 (
3%) 2 e.g. 0.123
0.500
0.003 (
0.6%) 2 0.456
1.000
0.004 (
0.4%) 3 1.123
1.500 (1 sign. fig. for A>2)
0.015 (
1%) 2 1.567
pH Meter
7.00
0.02 ~3 e.g. 6.123
Electronic Pressure Sensor
1.0 atm (760 torr)
0.0005 atm (
0.4 torr) 3-4 e.g 826.4 torr
Constant Current Power Supply
0.400 amp
0.0004 amp (
0.1 %) 3 0.4162 amp
* Spectro-Viz plus photometric accuracy is 13%, but standard curve calibration decreases the systematic error to
approximately equal the averaged precision (about 3 sign. figures), assuming the range of A is 0.1 to 1.0.
