Overview
This lecture covers the concepts of accuracy, precision, and types of measurement errors, along with methods to estimate and report errors and uncertainties in experimental physics measurements.
Accuracy vs. Precision
- Accuracy is how close a measured value is to the true or accepted value.
- Precision is how similar repeated measurements are to each other, regardless of closeness to the true value.
- Measurements can be precise but not accurate, or accurate but not precise.
- The best results are both accurate and precise.
Types of Errors in Measurement
- Blunders (Personal Errors): Errors due to carelessness or accidents, often resulting in anomalous data.
- Systematic Errors: Consistent errors caused by flaws in equipment or experimental procedure; affect accuracy but not precision.
- Sources include environmental, observational, or instrumental issues.
- Offset/zero error is a common systematic error (e.g., uncalibrated scale).
- Random Errors: Unpredictable variations due to uncontrollable conditions; mainly affect precision.
- Reading error is a type of random error occurring during direct measurement estimation.
Evaluating Accuracy and Precision
- Absolute Error: |Measured Value – True Value|
- Percent Error: (Absolute Error / True Value) × 100%
- Percent Difference: |Value1 – Value2| / [(Value1 + Value2)/2] × 100%; measures precision between two values.
Statistical Tools for Data Analysis
- Mean (Average): Sum of measurements divided by the number of measurements; considered the most probable value.
- Variance: Average of squared differences from the mean; measures data spread.
- Standard Deviation: Square root of variance; quantifies data dispersion and is used as uncertainty.
Reporting Measurements with Uncertainty
- Measurement is reported as Mean ± Standard Deviation.
- The true value is likely within the range of (Mean – SD) to (Mean + SD).
- Round uncertainty to one significant figure for clarity.
Example Calculations
- Use absolute error and percent error to compare experimental and true values.
- Use percent difference to assess consistency between repeated measurements.
- Calculate variance and standard deviation from a set of data for uncertainty estimation.
Key Terms & Definitions
- Accuracy — Closeness of a measurement to the true value.
- Precision — Consistency of repeated measurements.
- Absolute Error — Absolute difference between measured and true values.
- Percent Error — Absolute error expressed as a percentage of the true value.
- Percent Difference — Difference between two values relative to their average, in percent.
- Variance — Average of the squared deviations from the mean.
- Standard Deviation — Square root of the variance; indicates spread and uncertainty.
- Blunders — Errors from mistakes or accidents.
- Systematic Error — Reproducible error from faulty equipment or methods.
- Random Error — Unpredictable error from uncontrolled variables.
Action Items / Next Steps
- Complete concept builder exercises on accuracy, precision, and types of errors.
- Submit answers to the Padlet link as instructed.
- Practice calculations for error, standard deviation, and reporting results with uncertainty.