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Cochran test
The Dixon and Grubbs tests are used to investigate extreme values within a data set. The Cochran test is used to compare the variances of data sets. The test compares the highest variance with the sum of the variances for all the data sets (if each data set contains only two values then the standard deviation (s) is replaced by the range (d) in the equation below). This test is commonly used for evaluating the variances of data sets supplied by laboratories participating in interlaboratory studies. The test statistic is calculated from:
where l is the number of data sets. If the calculated value exceeds the critical value the largest variance is considered to be inconsistent with the variances of the other data sets. Some critical values for the Cochran test, at the 95% confidence level, are shown below. n is the number of values in each data set.
|
Critical values for the Cochran test (95% confidence level) |
l |
n = 2 |
n = 3 |
n = 4 |
n = 5 |
2 |
0.998 |
0.975 |
0.939 |
0.906 |
3 |
0.967 |
0.871 |
0.798 |
0.746 |
4 |
0.906 |
0.768 |
0.684 |
0.629 |
5 |
0.841 |
0.684 |
0.598 |
0.544 |
6 |
0.781 |
0.616 |
0.532 |
0.480 |
7 |
0.727 |
0.561 |
0.480 |
0.431 |
8 |
0.680 |
0.516 |
0.438 |
0.391 |
9 |
0.638 |
0.477 |
0.403 |
0.358 |
10 |
0.602 |
0.445 |
0.373 |
0.331 |
15 |
0.471 |
0.335 |
0.276 |
0.242 |
20 |
0.389 |
0.270 |
0.221 |
0.192 |
Last modified on
14 January 2009.