which contains 95.5% of the relevant measurements. Some workers believe this limit is too wide, and
regard the Q-test at a 90% confidence level to be a more acceptable alternative. A rejection quotient Q
is defined as
where xn is the questionable result in a set x 1 , x 2 , x 3 ,... , xn. Q is calculated for the questionable data and
compared with a table of critical values (Table 2.2). The result is rejected if Q (experimental) exceeds Q
(critical).
Table 2.2 Critical values of Q at the 90% confidence level
Number of results Qcrit(90% confidence)2 —3 0.944 0.765 0.646 0.567 0.51
8 0.479 0.4410 0.41The Analysis of Data
Once the reliability of a replicate set of measurements has been established the mean of the set may be
computed as a measure of the true mean. Unless an infinite number of measurements is made this true
mean will always remain unknown. However, the t-factor may be used to calculate a confidence
interval about the experimental mean, within which there is a known (90%) confidence of finding the
true mean. The limits of this confidence interval are given by:
where is the experimental mean, t is a statistical factor derived from the normal error curve (values in
Table 2.3), s is the estimated standard deviation and N is the number of results.
Example 2.1
If the analysis of a sample for iron content yields a mean result of 35.40% with a standard deviation of
0.30%, the size of the confidence interval will vary inversely with the number of measurements made.
For two measurements, the confidence interval (90%) is