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The Q test (a test for rejection of discordant data)


In some groups of five replicates, one value can be rejected. There is a test for this called the Q test, which is valid on samples of 3 to 10 replicates.  To perform the Q test, calculate the quantity Q, which is the ratio of [the difference between the value under suspicion and the next closest value] to [the difference between the highest and lowest value in the series].  Compare Q with the critical value for Q (below), which for 5 observations is 0.64.  If Q is greater than 0.64, the suspect measurement may be rejected.  Otherwise, it  must be retained.

For example, for values 1,2,3,4,9, if we wanted to test "9", we would take (9-4)/(9-1)=5/8 =0.625, which is less than 0.64, so we'd have to keep the 9. 

On the other hand, for the values, 3,3,4,4,9, if we wanted to test "9", we would take (9-4)/(9-3)=5/6 =0.833, which is greater than 0.64, so we can throw the 9 out.

Only one value in a small (defined as 3-10 values) group can be removed by this test. If you have more than one "wild" value, you just have a group of data with a lot of scatter, and you need to keep them all.

We perform the Q test on the total amounts of each lipid class, then eliminate a sample from our analysis of that the lipid species in that class if it doesn't meet the test.  

Qc (90%) (Critical values of Q) for sample sizes of 3-10 (taken from Shoemaker, J.P., Garland, C.W. and Steinfeld, J.I., "Experiments in Physical Chemistry", McGraw-Hill, Inc., 1974, pp. 34-39; this is also the reference for information about the Q test):

3                    0.94

4                    0.76

5                    0.64

6                    0.56

7                    0.51

8                    0.47

9                    0.44

10                0.41

 Copyright 2005 @ Kansas Lipidomics Research Center , Kansas State University.
 design by Prashanth Palakollu.

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Page last updated November 25, 2005