Error Analysis and Statistical Spread of Data

Errors & Uncertainty Bounds 

• There are two types of Error
  • Systematic Error
    • Occurs as a result as a flaw in the experiment design or apparatus
    • Cause the measured values to be consistently higher or lower than the actual value
    • They cannot be reduced by conducting repeated trails
    • Examples
      • Reading from the top of the meniscus when measuring volume
      • Forgetting to zero a mass balance
  • Random Error
    • Caused by unpredictable changes in the experiment. There is an equal probability of the measured value being too high or too low
    • Example
      • Changes in the environment during the experiment
    • Can be reduced by conducting repeated trails & by using a more precise apparatus
• When we talk about error we always consider Accuracy which is how close the measured values is from the actual value is made of two components
  • Bias
    • A measure of how far the expected value of the estimate is from the true value of the parameter
  • Precision
    • The smallest quantity that can be measured
• Random Fluctuations are governed by some statistics, MOST physical phenomena follow a Gaussian or Normal Distribution.

Error/Uncertainty Propagation
Say we have a value that is dependent on multiple variable which each have their own uncertainties associated with their values. How can we find the uncertainty of this dependent variable