Uncertainties and errors in measurement and results

Uncertainties and Errors in Measurements and Results

Uncertainty refers to the estimate of how much a measured or calculated value may deviate from the true value.
Uncertainty may be due to systematic errors (errors that consistently affect results in the same way) or random errors (errors that vary in an unpredictable manner).
Common sources of uncertainty include limitations of measuring instruments, operator error, and changes in the experimental environment.

Uncertainty is usually expressed as a range of values, e.g., 7.5 ± 0.2, where the reading is 7.5 and the uncertainty is ± 0.2.
Absolute uncertainty refers to the magnitude of the uncertainty, without considering the size of the measurement. It is usually expressed as ± some value.
Percentage uncertainty is absolute uncertainty expressed as a percentage of the measured value. It helps to compare uncertainties of different measurements.

Uncertainty propagation refers to how uncertainties of individual measurements combine to affect the uncertainty of the final result.
In addition or subtraction, absolute uncertainties add up.
In multiplication or division, percentage uncertainties add up.
In raising to a power, the percentage uncertainty multiplies by the power.

Systematic errors consistently affect outcomes in a predictable direction. Causes include poorly calibrated equipment, biased observers, or environmental conditions.
Random errors vary unpredictably, balancing out in the long term. Causes include fluctuations in readings, or environmental changes.
Systematic errors cause a lack of accuracy, while random errors cause a lack of precision. Accuracy reflects how close measurements are to the true value, while precision reflects how close repeated measurements are to each other.

Minimising uncertainties and errors can be achieved by repeating measurements, improving experimental techniques, or using better measuring equipment.
Statistical analysis can also help manage uncertainties, such as calculating the mean and standard deviation of multiple measurements.
It’s important to consider uncertainties and errors when interpreting results, and always express final results with the appropriate level of uncertainty.