Uncertainty

Uncertainty in Physical Measurements

(C) David M. Harrison 2013-2016

based on Guide to the Expression of Uncertainty in Measurement (GUM)

 

Module 1 - UM

Statistics of rolling a pair of dice, including an Activity of repeating the roll of dice 36 times. The module introduces:

  • Histograms
  • Probability distributions
  • Triangular probability distributions
  • The mean or average
  • The deviation
  • The variance

The modules also include links to videos using the computing environment (Python or Excel) for analysis of the data.

Materials
Uncertainty in Physical Measurements Module 1 - Excel Version
Student Guide
Uncertainty in Physical Measurements Module 1 - Python Version
Student Guide
Uncertainty Module 1 - Equipment List
Equipment List and Setup

Module 2 - UM

Uncertainty associated with digital instruments, including an Activity of measuring the diameter of a coin with a digital caliper. The module introduces:

  • Rectangular or uniform probability distributions
  • The standard deviation
  • The uncertainty associated with a measurement
  • Accuracy
  • Quadrature

It also discusses significant figures in an experimental context.

Materials
Uncertainty in Physical Measurements Module 2
Student Guide
Uncertainty Module 2 - Equipment List
Equipment List and Setup

Module 4 - UM

Uncertainty associated with repeated measurements that do not give the same values. It includes an Activity of measuring the time it takes a piece of paper to fall to the floor, and another Activity of measuring the ratio of the circumference to the radius of a number of metal hoops. The module introduces:

  • Scattered or dispersed measurements

  • Bell-shaped curves, also called Gaussian distributions or normal distributions
  • Gaussian probability distributions.
  • The uncertainty in the estimated standard deviation
  • Propagation of uncertainties
  • The uncertainty in the mean

A 10 minute PowerPoint review of bell-shaped curves that is useful after the students have read the Module but before they begin work on it. Primarily intended for instructors.

Materials
Uncertainty in Physical Measurements Module 4
Student Guide
Uncertainties Module 4 - short version
Student Guide
Uncertainty Module4 - Equipment List
Equipment List and Setup

Module 5 - UM

This Module is mostly concerned with fitting data to models, both by hand and by using least-squares techniques. It emphasises the visual display of data. The module introduces:

  • Independent and dependent variables of a dataset
  • Residuals of a fit
  • Sum of the squares of the residuals
  • Method of least squares
  • Degrees of freedom of a fit
  • Chi-squared
  • Effective variance method

Materials
Uncertainty in Physical Measurements Module 5 Student Guide
Student Guide
Uncertainty Module 5 - Equipment List
Equipment List and Setup

Module 6 - UM

Miscellaneous topics that don't fit nicely into the previous Modules. The Sections are:

  1. Confidence Intervals
  2. Uncertainty in a Count
  3. Systematic Effects and Calibration
  4. Outliers and Robust Estimators
  5. Accepted Values

The Module includes an Activity of calibrating a force sensor, and another Activity using robust measures of data to determine the period of a pendulum.

Materials
Uncertainty in Physical Measurements Module 6
Student Guide
Uncertainty Module 6 - Equipment List
Equipment List and Setup