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Precision is related to reproducibility and repeatabilityRepeatability — the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; andReproducibility — the variation arising using the same measurement process among different instruments and operators, and over longer time periods.
Accuracy refers to the agreement between a measurement and the true or correct value. It is meaningless unless the true value is known.Only refers to the agreement between the measured value and the expected value.Does not tell you about the quality of the instrument.A stopped clock is accurate at least twice each day.
Refers to the combination of both an accurate and precise measurement.A well designed procedure and well selected apparatus should produce a result that is valid.
This is because it is impossible to make an exact measurement.The degree of wrongness depends upon how the experiment was conducted, and how the data was analyzed.Error isthe reason why the measured value and ‘reference value’ don’t agree.is an unavoidable consequence of having to measure thingsis manageableshould not be attributed to “human error” – it’s not a mistake
Measurements will bounce around a central (average) valueDue to lack of resolution of the measuring deviceManage this by doing multiple trials (3 to 5)
Will push values in one direction (all measurements will be too high or too low).Can be due to poor calibration, improper use, ignoring outside influences that are quite significantManage by being careful
Find error sources that affect the outcome
(what part of the materials/apparatus made your results not 100% correct)Determine how you know they will affect the outcome
(give reasons why that tool wasn’t perfect)Determine how significant the effect will be
(big difference, small difference)By the end of the year, I would like you to try to estimate the size of the effect.
(1%, 5%, 10%)Give suggestions to improve the quality of your measurements (equipment or process changes)
The certainty of a measurement device is limited by its resolution. Its resolution is given by the value of the smallest graduations (markings) displayed on the device. We state the uncertainty as ± (plus or minus) half of the smallest marked value.All measurements are stated to the values readable on the device, plus one more.The above ruler has graduations (markings) every whole unit.
The uncertainty is half of that, (or 0.5 cm).We can be certain that the value is at least 2 cm and then we estimate an extra digit to come up with a length of 2.5 cm. That last digit is uncertain, but significant.We would state this result as 2.5 cm ± 0.5 cmThe above ruler has graduations (markings) every tenth (0.10 cm) of a unit.The uncertainty is half of that, (or 0.05 cm).We can be certain that the value is at least 2.5 cm and then we estimate an extra digit to come up with a length of 2.55 cm. That last digit is uncertain, but significant.We would state this result as 2.55 cm ± 0.05 cm
Set up apparatus. Run through a “trial”. Look for sources of error.
How can you make the method more repeatable?How can you reduce the impact of the uncertainty that exists in your measurements?Can you change how you are collecting a measurement?Would a different measuring device help you get more significant digits in your measurement?Would observing over a longer time interval make it easier to find the start or stop of an event?Can you define a method that eliminates the measurement of time entirely? (Possible in some, but not all cases, it depends on whether or not the time is a desirable quantity)
Measurement Systems
Precision, Accuracy, & Validity
When designing an experiment, we develop our procedure and select our apparatus to ensure that the measurements we make are:
Precise
Accurate
Valid
Error
All measurements are wrong!
Random Error
Systematic Error
Reporting Error
Certainty (and uncertainty)
Tips for Developing an Experiment
Ask yourself:
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