Sources of Uncertainty (AQA A Level Physics)

• Measurements of quantities are made with the aim of finding the true value of that quantity
• In reality, it is impossible to obtain the true value of any quantity as there will always be a degree of uncertainty
• The uncertainty is an estimate of the difference between a measurement reading and the true value
• Random and systematic errors are two types of measurement errors that lead to uncertainty

Random error

• Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions
• This affects the precision of the measurements taken, causing a wider spread of results about the mean value
• To reduce random error:
  • Repeat measurements several times and calculate an average from them

Systematic error

• Systematic errors arise from the use of faulty instruments used or from flaws in the experimental method
• This type of error is repeated consistently every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained
• To reduce systematic errors:
  • Instruments should be recalibrated, or different instruments should be used
  • Corrections or adjustments should be made to the technique

Representing precision and accuracy on a graph

Zero error

• This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero
• This introduces a fixed error into readings which must be accounted for when the results are recorded

Precision

• Precise measurements are ones in which there is very little spread about the mean value, in other words, how close the measured values are to each other
• If a measurement is repeated several times, it can be described as precise when the values are very similar to, or the same as, each other
• The precision of a measurement is reflected in the values recorded - measurements to a greater number of decimal places are said to be more precise than those to a whole number

Accuracy

• A measurement is considered accurate if it is close to the true value
• The accuracy can be increased by repeating measurements and finding a mean of the results
• Repeating measurements also helps to identify anomalies that can be omitted from the final results

The difference between precise and accurate results

Repeatability

• A measurement is repeatable if the original experimenter repeats the investigation using the same method and equipment and obtains the same results

Reproducibility

• A measurement is reproducible if the investigation is repeated by another person, or by using different equipment or techniques, and the same results are obtained

Resolution

• Resolution is the smallest change in the quantity being measured of a measuring instrument that gives a perceptible change in the reading
• For example, the resolution of a wristwatch is 1 s, whereas the resolution of a digital stop-clock is typically 10 ms (0.01 s)
• In imaging, resolution can also be described as the ability to see two structures as two separate structures rather than as one fuzzy entity

Good resolution and poor resolution in an ultrasound scanner. The good image manages to resolve the two objects into two distinct structures whereas the poor image shows one fuzzy entity.