Physics Practicals

Uncertainty

Uncertainty in Physical Measurements

(C) David M. Harrison 2013-2016

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

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 Introduction
Student Guide
Uncertainty Module4 - Equipment List
Equipment List and Setup

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

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