Uncertainties and Methods

• Uncertainty in a reading: ± half the smallest division
• Uncertainty in a measurement: at least ±1 smallest division
• Repeated Data Uncertainty: mean ± (range)/2
• Combining uncertainties:

  • Adding / subtracting data = Add the absolute uncertainties
  • Multiplying/dividing data = Add the percentage uncertainties
  • Raising to a power = Multiply the percentage uncertainty by the power
• Percentage Uncertainty: uncertainty/value x 100
• Percentage uncertainty:

  • (Best Gradient - Worst Gradient)/Best Gradient x 100%
  • (Best y-intercept - Worst y-intercept)/Best y-intercept x 100%
• Absolute uncertainty: uncertainty given as a fixed quantity
• Fractional uncertainty: uncertainty given as a fraction of the measurement
• Percentage uncertainty: uncertainty as a percentage of the measurement
• To reduce percentage and fractional uncertainties, you need to measure larger quantities
• Random errors:

  • affects precision --> causes differences in measurements and a spread about the mean
  • cannot get rid of all random errors
• Reducing random errors:

  • Take at least 3 repeats and calculate a mean - allowing for anomalies to be identified
  • Use computers/data loggers to reduce human error and enable smaller intervals
  • Use appropriate equipment (e.g. a micrometer has a higher resolution [0.1mm] than a ruler [1mm])
• Reducing systematic errors:

  • Calibrate apparatus by measuring a known value, if the reading is inaccurate then the systematic error is easily identified
  • In radiation experiments, correct for the background radiation by measuring it beforehand and excluding it from the final results
  • Read the meniscus (the central curve on the surface of a liquid) at eye level to reduce parallax error and use controls in experiments
• Precision: Precise measurements are consistent, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate
• Repeatability: If the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable
• Reproducibility: If the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is reproducible
• Resolution: The smallest change in the quantity being measured that gives a recognisable change in reading
• Accuracy: A measurement close to the true value is accurate
• Systematic errors:

  • Affect accuracy
  • Occurs due to the apparatus or faults in the experimental method
  • Systematic errors cause all results to be too high or too low by the same amount each time
  • i.e. a balance that isn't zeroed correctly (zero error) or reading a scale at a different angle (parallax error)
• Types of data:

  • Discrete: only certain values can be taken, e.g. number of objects. Display on scatter graphs and bar charts
  • Continuous: can take any value on a scale e.g. current in a circuit. Display on line or scatter graph
  • Categoric: values that can be sorted into categories e.g. types of material. Display on a pie or bar chart
  • Ordered: data that can be put in ordered categories e.g. low, medium, high. Bar charts can display ordered data