Q TEST
What is Q Test?
Generally, Q test is a rejection of a result. It is one of
the most statistically correct for a fairly small
number of observations and is recommended when a
test is necessary.
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What it is used for?
1. The Q test is used to determine whether an
“outlier” or suspected number is due to a
determinate error. If it is not, then it falls within
the expected random error and should be
retained. ( Gary D. Christian, Anal. Chem. Sixth
Edition.)
In statistic, Q test is used for identification and
rejection of outliers. This test should be used
sparingly and never more than once in a data
set.
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The ratio Q is calculated by arrange the data in
decreasing order of numbers.
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To apply a Q test for bad data, arrange the data
in order of increasing values and Q is as defined:
Qgap
a
Q
or Q 
w
Qrange
Where,
Qgap or “a” is the absolute difference between the
outlier in question (suspect number) and the closest
number to it (nearest neighbor).
• Qrange or “w” is the difference between the highest
number and the lowest number.
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If Qcalculated  Qtable then reject the
questionable point.
But, if Qcalculated < Qtable then the questionable
point should not be rejected.
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EXAMPLE
For the data:
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0.189, 0.169, 0.187, 0.183, 0.186, 0.182,
0.181, 0.184, 0.181, 0.177.
Determine if it can be ascribed to accidental
error, at the 90% confidence level.
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SOLUTION:
Arranged it in increasing order:
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0.169,0.177,0.181,0.181,0.182,0.183,0.184,0.186,0.187,
0.189
Thus, the outlier (suspected no.) is 0.169.
Then, calculate Q:
a 0.177  0.169
Q 
 0.400
w 0.189  0.169
From the tabulated table, the 10 observations at
90% confidence level is 0.412.
Since, 0.4 (Qcal) < 0.412 (Qtable). Therefore, 0.169
which is the outlier should not be rejected and
can be ascribed to random error.
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EXAMPLE 2
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A set of chloride analyses on separate aliquots of a
pooled serum were reported:
103, 106, 107, and 114 meq/L.
One value appears suspect. Determine if it can be
ascribed to accidental error, at the 95%
confidence level.
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SOLUTION:
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The suspect result is 114 meq/L.
a 114  107 meq / L 7
Q 
  0.64
w 114  103meq / L 11
From the tabulated table, the fourth observation at
95% confidence level is 0.829.
Since, 0.64 (Qcal) < 0.829 (Qtable), the suspected
number may be ascribed to random error and
should not be rejected.
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FINALLY,
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The Q test should not be applied to three data
points if two are identical.
In that case, the test always indicate rejection of
the third value, regardless of the magnitude of
the deviation, because “a” is equal to “w” and
Qcalc is always equal to 1.
The same obviously applies for three identical
data points in four measurements and so forth.
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