Measurement and Method

How a Physical Result Is Made, Checked and Reported in 14 chapters — from “What a measured value is: quantities, units and the SI” to “Writing the result, and the integrity of the data behind it”.

Chapters

  1. What a measured value is: quantities, units and the SI
    • A physical quantity and its unit
    • The SI defining constants since 2019
    • Prefixes and notation in unit conversions
    • The measurand and the true value
    • Significant figures and rounding a result
    • Summary
    • Problems
  2. What dimensions decide before you measure anything
    • Dimension and dimensional homogeneity
    • Dimensional derivation of a pendulum's period
    • Dimensionless groups and what to plot
    • Scaling laws on log-log axes
    • Order-of-magnitude estimation and the dimensional check
    • Summary
    • Problems
  3. The instrument: resolution, sensitivity, calibration and traceability
    • Resolution, sensitivity and range
    • Zero errors, drift and hysteresis
    • Reading an instrument specification
    • Calibration against two fixed points
    • Traceability to the defining constants
    • Loading by the instrument
    • Summary
    • Problems
  4. Repeated readings: scatter, the mean and the standard error
    • The distribution of readings
    • The mean and the sample standard deviation
    • The standard error of the mean
    • Random and systematic effects
    • The number of readings worth taking
    • What a single reading is worth
    • Reporting a mean
    • Problems
  5. Propagating uncertainty into the quantity you actually want
    • Resistivity as an output quantity
    • The sensitivity coefficient
    • Addition in quadrature
    • Shortcut rules for sums, products and powers
    • Propagation in practice and the dominant term
    • Correlated inputs
    • The correlation coefficient and shared inputs
    • Failure of the first-order rule
    • Problems
  6. Type A, Type B and the uncertainty budget
    • Standard uncertainty and the measurement model
    • Type A evaluation
    • Type B evaluation and the rectangular distribution
    • Combined standard uncertainty and the uncertainty budget
    • The Gaussian distribution
    • Expanded uncertainty and Student's t factor
    • Limits of a budget
    • Problems
  7. Do two results agree? Comparison, consistency and outliers
    • The discrepancy between two results
    • The consistency ratio
    • Correlated comparison of results sharing a calibration
    • Meaning of agreement and statistical significance
    • Outliers and Chauvenet's criterion
    • Documented exclusion of a suspect reading
    • An inconsistent set of results
    • Summary
    • Problems
  8. Counting experiments: Poisson statistics and the root-n rule
    • A count as a random variable
    • Binomial counting and the Poisson distribution
    • The root-n rule and the count rate
    • Background subtraction and its price
    • Counting time and its division
    • Dead time
    • Small counts and a check on the apparatus
    • Summary
    • Problems
  9. Graphs, straight lines and least squares
    • Nine resistances and graph conventions
    • Error bar convention and a bad graph
    • Linearisation of curved relations
    • Least-squares principle and the normal equations
    • Parameter uncertainties of slope and intercept
    • Weighted fit and weighted mean
    • Residual plot, chi-squared and the inflation factor
    • Summary
    • Problems
  10. Monte Carlo and the bootstrap: uncertainty by sampling
    • The simulated experiment
    • Transformation method and acceptance-rejection
    • Monte Carlo propagation
    • The bootstrap
    • Trial numbers and limits of simulation
    • Summary
    • Problems
  11. Designing the measurement: noise, averaging, null and differential methods
    • Noise and the signal-to-noise ratio
    • Signal averaging and the optimum averaging time
    • The null method
    • The differential method
    • The design budget
    • Summary
    • Problems
  12. Running it: troubleshooting, the systematics hunt, safety and the record
    • Sixty nanoseconds and the first switch-on
    • Bisection and substitution
    • The change-it-and-see test
    • The stopping rule and blind analysis
    • Laboratory notebook and raw data file
    • Laboratory safety
    • Summary
    • Problems
  13. Models, idealisation and what a measurement is evidence for
    • Model and idealisation in the pendulum
    • Quantified idealisation and the budget
    • Measurement as evidence
    • Auxiliary assumptions behind a comparison
    • Theory choice without a decisive experiment
    • An audit of idealisations
    • Reading a claim
    • Summary
    • Problems
  14. Writing the result, and the integrity of the data behind it
    • The purpose of a report
    • Report structure
    • Tables and figures
    • Stating the conclusion
    • Research misconduct
    • Selective reporting
    • Authorship and credit
    • The record as defence
    • Summary
    • Problems