11.1 Uncertainties and errors in measurements and results
Qualitative & Quantitative Analysis
- Analysis of data can be classified into two types
- Qualitative Analysis
- Comes from observations and non-numerical methods
- Quantitative Analysis
- Comes from measurements and always associated with uncertainties determined by either the apparatus and human limitations such as reaction times and sight
- In science, numerical data is divided into two types
- Data with exact numbers (no uncertainty)
- Data with inexact numbers (Degree of uncertainty involved)
Precision vs Accuracy
- Precision: Closeness of agreement between interdependent test results
- Accuracy: Closeness of agreement between the result of measurement and the true value
- Number of digits reflecting precision of a given measurement
- Sometimes it is useful to write in Scientific notation
- Here are some examples:
- Some rules for significant figures in calculation
- For multiplication or division: Result should be expressed based on measurement with smallest number of significant figures.
- For addition or subtraction: Result should be expressed based on measurement with smallest number of decimal places
- (A simple rule on the side is that your final answer should be expressed in the number of significant figures of the measurement with the lowest number of significant figures)
- Every measurement has a degree of uncertainty with it called experimental error
- There are two types of experimental error
- Systematic error: A flaw in experimental design or methodology. This affects the accuracy of the results.
- Random error: Occur because of uncontrolled variables. Cannot be eliminated. This affects the precision of the results.
Absolute and Relative Uncertainty
- Absolute Uncertainty is the margin of uncertainty associated with the result from a measurement.
- Its symbol is given by ΔA
- Relative Uncertainty is the ratio comparing the size of the absolute uncertainty.
- Relative uncertainty = ΔA / A
- All experimental results should be reported in form:
- Experimental result = (A ± ΔA) units