error_analysis - Error Analysis Expressing uncertainty in...

Error Analysis
Expressing uncertainty in
measurements of physical
properties

Types of Errors
• Systematic Errors
– All Errors in Same Direction
– Instrumental bias
– Misreading/misuse of instrument
– Miscalibration
– Contamination
• Random Errors
– Errors in Different Directions
– Intrinsic limitations of instrument/measurement sensitivity
– Limitations of ability to interpret output
– Mechanical/electronic limitations –e.g., stability
• Model Errors
– Flawed assumption in experimental design

Examples
• Balance not tared
• Reading wrong scale on gauge
• Determine molar mass (MM) of a gas from
the relationship MM = (m/V)(RT/P)
• Stopwatch timing of events
• Unsuspected background peak in
spectrum

Experimental Results
• Directly measured property
– Examples: mass, volume, time
– Often measured multiple times
• Parameters of an assumed functional relationship
(e.g. y = mx + b)
– Absorptivity from graph of measured absorbance vs.
concentration
• Calculated value
– Examples: molar mass from P, V and T data
• Experimental results are often compared to
expected/theoretical values

Calculating Accuracy
100 x
TrueValue
lue MeasuredVa TrueValue
or PercentErr
−
=

Accuracy vs. Precision