Read through the summarized points below carefully. As a last exercise, continue with
the mixed exercises (link below), which summarize everything that you (should) have learned
today.
The normal distribution
- Many experimental errors are normally distributed
- They can be characterised by a mean value and a standard deviation
- The mean describes the location
- The standard deviation describes the spread around the mean
- Random errors are related to the standard deviation
- Systematic errors are related to the difference between the mean and
the (unknown) true value (the bias).
Confidence intervals
- The larger the spread around a central value, the wider a confidence
interval will be
- A 95% confidence interval for an individual value will contain
the next experimental value with a probability of 95%
- A crude estimate of a 95% confidence interval is the mean plus
or minus twice the standard deviation
- A crude estimate of a 99% confidence interval is the mean plus
or minus three times the standard deviation
- Confidence intervals for the mean are narrower than confidence
intervals for individual values since errors cancel out
- The standard deviation of the mean is the standard deviation of
the individual values divided by the square root of the number of measurements
Least squares regression
- The linear relationship between two variables x and y
can be described by the abcissa and the slope of the optimal straight line
- Standard errors for abcissa and slope can be calculated, and
therefore confidence intervals too
- It is assumed that the error in x is much smaller than the
error in y
- Residuals are assumed to be independent and normally distributed
with constant variance
- Regression lines may be used for calibration: the calibration line
is set up using a set of calibration samples and the concentration in
an unknown sample can be predicted
- Regression lines can be used to compare methods
As a final test, prepare yourself for the
mixed exercises.