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.

Q _c (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):

Number of replicates	Q critical value
3	0.94
4	0.76
5	0.64
6	0.56
7	0.51
8	0.47
9	0.44
10	0.41