Precision

Examples of Precision in the following topics:

• Accuracy, Precision, and Error

  • Accuracy is how closely the measured value is to the true value, whereas precision expresses reproducibility.
  • Measurements can be both accurate and precise, accurate but not precise, precise but not accurate, or neither.
  • This is an easy to understand introduction to accuracy and precision.
  • On this bullseye, the hits are all close to the center, but none are close to each other; this is an example of accuracy without precision.
  • Describe the difference between accuracy and precision, and identify sources of error in measurement

• Accuracy vs. Precision

  • In order to be valid, data must be both accurate and precise.
  • If their data is both accurate and precise, this gives them confidence that it is valid.
  • In this way, measurements can be quite precise, but not accurate.
  • Note that measurements can also be accurate, but not precise.
  • Discuss why data must be both accurate and precise in order to be valid

• Motor Units

  • Precision is inversely proportional to the size of the motor unit.
  • Thus, small motor units can exercise greater precision of movement compared to larger motor units.
  • For instance, thigh muscles, responsible for large powerful movements, can have a thousand fibers in each unit, while eye muscles, requiring small precise movements, might only have ten.
  • There are often multiple sizes of motor unit within a motor pool as a means of modulating the precision and force produced by a single muscle.
  • For example, a small motor unit in the biceps can be activated for small precise movements, while a larger motor unit can be activated to facilitate more forceful actions.

• Precision

  • This kind of precise writing will help your audience understand your argument.
  • Specific words help your readers understand precisely what you mean in your writing.
  • Writing with precision helps hold your audience's attention.
  • Sometimes it is best to keep your writing simple and precise.
  • The more precise your writing is, the easier it will be for your reader to understand your argument.

• Beats and Wide Tuning

  • A piano tuner works by listening to and timing these beats, rather than by being able to "hear" equal temperament intervals precisely.
  • It should also be noted that some music traditions around the world do not use the type of precision tunings described above, not because they can't, but because of an aesthetic preference for wide tuning.
  • In these traditions, the sound of many people playing precisely the same pitch is considered a thin, uninteresting sound; the sound of many people playing near the same pitch is heard as full, lively, and more interesting.
  • Some music traditions even use an extremely precise version of wide tuning.
  • In some types of gamelans, pairs of instruments are tuned very precisely so that each pair produces beats, and the rate of the beats is the same throughout the entire range of that gamelan.

• Chance Error

  • Random errors are due to the precision of the equipment , and systematic errors are due to how well the equipment was used or how well the experiment was controlled .
  • A random error makes the measured value both smaller and larger than the true value; they are errors of precision.
  • These are errors incurred as a result of making measurements on imperfect tools which can only have certain degree of precision.
  • This target shows an example of low accuracy (points are not close to center target) but high precision (points are close together).
  • This target shows an example of high accuracy (points are all close to center target) but low precision (points are not close together).

• Significant Figures

  • Significant figures are digits which contribute to the precision of a number.
  • Significant figures of a number are digits which contribute to the precision of that number.
  • Numbers that do not contribute any precision and should not be counted as a significant number are:
  • This convention clarifies the precision of such numbers.
  • For example, if a measurement that is precise to four decimal places (0.0001) is given as 12.23, then the measurement might be understood as having only two decimal places of precision available.

• Problems

• Explanation, Prediction and Storytelling

  • Whether explaining or predicting, science places value on precision and rigor of the process.
  • It is also necessary to avoid attempts at precision and rigor that are not possible.
  • [Mayer's book]...is a plea for a more modest economics that recognizes the inherent difficulty of making precise and indubitable statements about the actual world, accepts that there is a trade-off between rigor and relevance.
  • An emphasis on rigor and precision may result in attempts to develop theories or models that are esoteric and of little interest to anyone other than the scientist-author.

• Quantum-Mechanical View of Atoms

  • Atoms in solid states (or, to be precise, their electron clouds) can be observed individually using special instruments such as the scanning tunneling microscope.
  • A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926.
  • One of the hydrogen's atomic transitions (n=2 to n=1, n: principal quantum number) has been measured to an extraordinary precision of 1 part in a hundred trillion.
  • This kind of spectroscopic precision allows physicists to refine quantum theories of atoms, by accounting for minuscule discrepancies between experimental results and theories.