Statistical Data Treatment

and Evaluation

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

interval (CI).

•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

calibration curves.

CONFINENCE LIMITS

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

Estimate of

A general expression for the confidence limits (CL) of a

single measurement

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

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