Measurement Certainty: How Certain Are You?
Polymer film with thickness variation.Copyright 2014 Ralph Cox, Rice University
Students learn about the statistical analysis of measurements and error propagation, reviewing concepts of precision, accuracy and error types. This is done through calculations related to the concept of density. Students work in teams to each measure the dimensions and mass of five identical cubes, compile the measurements into small data sets, calculate statistics including the mean and standard deviation of these measurements, and use the mean values of the measurements to calculate density of the cubes. Then they use this calculated density to determine the mass of a new object made of the same material. This is done by measuring the appropriate dimensions of the new object, calculating its volume, and then calculating its mass using the density value. Next, the mass of the new object is measured by each student group and the standard deviation of the measurements is calculated. Finally, students determine the accuracy of the calculated mass by comparing it to the measured mass, determining whether the difference in the measurements is more or less than the standard deviation.
Measurement, and the ability to determine the accuracy and precision of any given measurement, is the basis of all science, technology and engineering. For instance, the ability to measure and produce mass market goods that precisely reproduce specific measurements enables the availability of inexpensive cables that reliably connect computers to printers. It also results in the manufacture of memory devices that plug easily into sockets of a motherboard. In this activity, students learn how to determine the certainty of their measurements, and then use the measurements to compute various variables. The statistics used in this activity form the basis for applications used across various fields of engineering and science, from determining whether a population has a higher rate of a certain illness, to proving that a photon can act like a particle. For many engineers, the accuracy and precision of the measurements in their designs affects public safety. For example, civil engineers who design structures such as buildings and bridges and mechanical and aerospace engineers who design vehicles such as cars, planes and spacecraft must ensure that all measurements are accurate so that their finished designs function correctly and safely.
After this activity, students should be able to:
- Demonstrate that a measurement is accurate and precise by citing specific proof from procedures and instruments used.
- Describe the difference between random and systematic errors, giving several examples of systematic errors and what can be done to avoid such errors.
- Calculate a random error using standard deviation, assuming that the measurements are normally distributed.
- Explain the difference between calculated and measured values.