Statistical Data Treatment
Experimentalist use statistical calculations to sharpen
their judgments concerning the quality of experimental
measurements. These applications include:
•Defining a numerical interval around the mean of a set
of replicate analytical results within which the
population mean can be expected to lie with a certain
probability. This interval is called the confidence
•Determining the number of replicate
measurements required to ensure at a given
probability that an experimental mean falls
within a certain confidence interval.
•Estimating the probability that (a) an
experimental mean and a true value or (b) two
experimental means are different.
•Deciding whether what appears to be an outlier
in a set of replicate measurements is the result of
a gross error or it is a legitimate result.
•Using the least-squares method for constructing
Confidence limits define a numerical interval around x
that contains with a certain probability. A confidence
interval is the numerical magnitude of the confidence
limit. The size of the confidence interval, which is
computed from the sample standard deviation, depends
on how accurately we know s, how close standard
deviation is to the population standard deviation .
Finding the Confidence Interval when s Is a Good
A general expression for the confidence limits (CL) of a
CL = x z
For the mean of N measurements, the standard error of
the mean, /N is used in place of
CL for = x z/N