Observations & Measurements
Accuracy: This refers to how close a measurement is to the true or accepted value of the quantity being measured. High accuracy implies that systematic errors have been minimized.
Precision: This describes the consistency or reproducibility of a set of measurements. A precise set of data has a very small spread or range around the mean value, indicating low random error.
The Relationship: It is possible for a measurement to be highly precise (consistent) but inaccurate (far from the truth), often due to a poorly calibrated instrument.
Random Errors: These cause unpredictable fluctuations in readings due to uncontrollable factors like environmental changes or human reaction time. They affect the precision of the data and can be reduced by repeating measurements and calculating a mean.
Systematic Errors: These are consistent, repeatable errors usually caused by faulty equipment (e.g., zero error on a scale) or a flawed experimental method. They affect the accuracy of the data and cannot be removed by averaging; instead, the instrument must be recalibrated or the method changed.
Zero Error: A specific type of systematic error where an instrument gives a non-zero reading when the actual value is zero. This value must be subtracted from all subsequent readings.
Absolute Uncertainty: For analogue instruments, the uncertainty is typically half the smallest scale division. For example, a ruler with mm divisions has an uncertainty of mm.
Percentage Uncertainty: This is calculated as . It provides a measure of the relative significance of the error.
Optimization: To minimize percentage uncertainty, scientists aim to measure larger values using the same equipment. For instance, measuring the thickness of sheets of paper and dividing by is more accurate than measuring a single sheet.
Definition: An anomaly is a data point that does not fit the general trend of the other results or replicates. It is often defined as a value that deviates from the mean by more than .
Identification: Anomalies are most easily spotted on a scatter graph as points that lie far from the line of best fit.
Management: When an anomaly is identified, it should be excluded from the calculation of the mean. If possible, the specific measurement should be repeated to determine if the anomaly was a one-off error.
Check the Units: Always ensure that measurements are recorded with their appropriate SI units. Forgetting units is a common way to lose marks in practical assessments.
Significant Figures: Ensure that calculated values (like means) are rounded to the same number of significant figures as the raw data used to calculate them.
Sanity Check: Evaluate if the percentage uncertainty is reasonable. If you calculate a error for a simple length measurement, re-check your decimal places or formula.
Reaction Time: In timing experiments, always acknowledge that human reaction time (typically to seconds) is a more significant source of uncertainty than the resolution of a digital stopwatch ( seconds).