Precision

The precision of a measurement characterizes the dispersion of results obtained when the same measurement is repeated several times under the same experimental conditions.

Discover FizziQ

How to measure it in class

With the FizziQ app, it is possible to quantify the precision of a sensor by repeating the same measurement.

Steps:

Open FizziQ and select the pressure sensor. Place the smartphone on the table and record pressure for 30 seconds without touching the device.
Export the data and calculate the mean and standard deviation of the series of measurements obtained.
Repeat the experiment by placing the smartphone in another location in the room. Compare the standard deviations obtained.
Interpret the results: the standard deviation represents the precision of the sensor under these conditions. Discuss factors that could affect this precision (vibrations, air currents, temperature).

Scientific activities on this topic

Several experiments easily achievable with a smartphone, tablet, or computer allow studying the precision of experimental measurements.

1: Evaluating sensor quality - Analysis of sensor precision: https://www.fizziq.org/en/activities/evaluate-the-quality-of-a-sensor/
2: Uncertainty - Analyzing measurement uncertainties: https://www.fizziq.org/en/activities/uncertainty/
3: Pendulum period - Build a device to precisely determine the period of a pendulum: https://www.fizziq.org/en/activities/period-of-a-pendulum/
4: Latitude and gravity - Measurement of gravitational constant g and its variation according to latitude: https://www.fizziq.org/en/activities/latitude-and-gravity/

Learn more

Precision, accuracy, and trueness according to ISO standard

The ISO 5725 standard rigorously defines these three concepts. Trueness is the closeness of the mean of measurements to the true value. Precision is the closeness of measurements to each other. Accuracy combines both: a result is accurate if it is both true and precise. This distinction is fundamental in metrology.

Repeatability and reproducibility

Precision breaks down into two sub-concepts. Repeatability concerns variations observed when the same operator repeats the measurement under the same conditions. Reproducibility concerns variations when different operators or different conditions are used. Reproducibility is always worse than repeatability.

Precision and number of measurements

Uncertainty on the mean decreases as 1/sqrt(n), where n is the number of measurements. Going from 1 to 4 measurements divides uncertainty by 2. Going from 4 to 16 measurements divides it again by 2. There is therefore a trade-off between time spent measuring and gain in precision.

Industrial applications

In industrial production, instrument precision determines manufacturing tolerances. A mechanical part intended for an aircraft engine requires precision on the order of a micrometer. In pharmacy, balance precision determines the dosage of active ingredients. Each field defines the minimum acceptable precision for its applications.

Formula

Precision is quantified by the standard deviation of repeated measurements:

sigma = sqrt[ sum((xi - x_bar)^2) / (n - 1) ]

Meaning: sigma: standard deviation (in the unit of the measured quantity) xi: value of measurement i x_bar: mean of the n measurements n: number of measurements made

Application examples

An archer whose arrows are grouped in the same spot is precise, even if they are not in the center
A GPS that always displays the same position within plus or minus 2 m is more precise than a GPS varying by plus or minus 20 m
A bathroom scale that displays 72.3 kg then 72.4 kg then 72.3 kg is precise
A manual stopwatch operated by a human is less precise than a photoelectric cell stopwatch
Body temperature measurement with a forehead thermometer is less precise than with a rectal thermometer

FAQ

Q: What is the difference between precision and accuracy? A: Precision measures the dispersion of results among themselves. Accuracy measures the deviation between the mean of results and the true value. An instrument can be precise without being accurate, and vice versa.

Q: How to improve measurement precision in class? A: You can average several measurements, stabilize experimental conditions, use a better quality sensor, or reduce sources of vibration and disturbance.

Q: How many measurements should be repeated? A: In practice, 5 to 10 measurements are sufficient to estimate precision in class. The more you repeat, the more reliable the standard deviation estimate.

Q: Does precision depend on the operator? A: Yes, especially for manual measurements. A trained operator generally obtains more precise results than a beginner.

Q: Can precision be better than resolution? A: By averaging many measurements, you can indeed achieve precision better than the instrument’s resolution, thanks to statistical averaging.

Accuracy - Uncertainty - Standard deviation - Resolution - Measurement noise - Reproducibility - Repeatability