The uncertainty of measurements
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This document discusses various sources of uncertainty in physics measurements, including incomplete definitions, unaccounted factors, environmental influences, instrument limitations, calibration errors, physical variations, drifts, response times, and parallax. It emphasizes that all measurements have some degree of uncertainty from multiple sources. Properly reporting uncertainty allows evaluation of experimental quality and comparison to other results. While the true value may not be known exactly, uncertainty analysis helps ascertain a measurement's accuracy and precision.
The uncertainty of measurements
- 1. THE UNCERTAINTY OF MEASUREMENTS General Physics I Erwin Marlon R. Sario
- 2. Common Sources of error in Physics Laboratory Experiment Incomplete definition (may be systematic or random) - One reason that it is impossible to make exact measurements is that the measurement is not always clearly defined.
- 3. Failure to account for a factor (usually systematic) –The most challenging part of designing an experiment is trying to control or account for all possible factors except the one independent variable that is being analyzed.
- 4. Environmental factors (systematic or random) - Be aware of errors introduced by your immediate working environment.You may need to take account for or protect your experiment from vibrations, drafts, changes in temperature, electronic noise or other effects from nearby apparatus.
- 5. Instrument resolution (random) - All instruments have finite precision that limits the ability to resolve small measurement differences. For instance, a meter stick cannot distinguish distances to a precision much better than about half of its smallest scale division (0.5 mm in this case).
- 6. Failure to calibrate or check zero of instrument (systematic) - Whenever possible, the calibration of an instrument should be checked before taking data. If a calibration standard is not available, the accuracy of the instrument should be checked by comparing with another instrument that is at least as precise, or by consulting the technical data provided by the manufacturer.
- 7. Physical variations (random) - It is always wise to obtain multiple measurements over the entire range being investigated. Doing so often reveals variations that might otherwise go undetected.These variations may call for closer examination, or they may be combined to find an average value.
- 8. Instrument drift (systematic) - Most electronic instruments have readings that drift over time.The amount of drift is generally not a concern, but occasionally this source of error can be significant and should be considered.
- 9. Lag time and hysteresis (systematic) - Some measuring devices require time to reach equilibrium, and taking a measurement before the instrument is stable will result in a measurement that is generally too low.
- 10. Parallax (systematic or random) -This error can occur whenever there is some distance between the measuring scale and the indicator used to obtain a measurement. If the observer's eye is not squarely aligned with the pointer and scale, the reading may be too high or low (some analog meters have mirrors to help with this alignment).
- 12. All measurements have some degree of uncertainty that may come from a variety of sources.The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis.
- 13. Personal errors come from carelessness, poor technique, or bias on the part of the experimenter.The experimenter may measure incorrectly, or may use poor technique in taking a measurement, or may introduce a bias into measurements by expecting (and inadvertently forcing) the results to agree with the expected outcome. Gross personal errors, sometimes called mistakes or blunders, should be avoided and corrected if discovered.
- 14. Properly reporting an experimental result along with its uncertainty allows other people to make judgments about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction.Without an uncertainty estimate, it is impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?"This question is fundamental for deciding if a scientific hypothesis is confirmed or refuted.
- 15. When we make a measurement, we generally assume that some exact or true value exists based on how we define what is being measured. While we may never know this true value exactly, we attempt to find this ideal quantity to the best of our ability with the time and resources available.
- 16. The uncertainty of a single measurement is limited by the precision and accuracy of the measuring instrument, along with any other factors that might affect the ability of the experimenter to make the measurement.
- 17. For example, if you are trying to use a meter stick to measure the diameter of a tennis ball, the uncertainty might be ± 5 mm, but if you used aVernier caliper, the uncertainty could be reduced to maybe ± 2 mm.
- 18. Estimating Uncertainty in Repeated Measurements. Example: The length of building was measured by the students 5 times.They got the following results: 22m, 24m, 23m, 24m and 27m. Find the average of trials: 22+24+23+24+27 = 120 120/5 =24 Uncertainty: (27-22)/2 = 2.5 Length of the building: 24±𝟑m