analytical results
The basis for accepting or rejecting an outlying analytical result is a statistical decision rather than a personal judgment call, most commonly made using the 4d rule or the Q-test, both of which compare a doubtful value’s deviation from the rest of the dataset against a defined statistical threshold before it can be discarded.
Unexpected laboratory results-Think before discarding
Your analytical results should be consistent if you adhere to the specified method and take all the prescribed experimental precautions. You may still be dismayed on seeing some outlying values and will be faced with the hard decision on inclusion or rejection of such values. The implication of your choice will not be of much significance if the number of observations is large as a single value will only have small effect on the mean value. However in small set of observations the impact can be significant.
Basic Statistics can come to your rescue in such situations.You will be able to base your judgment on a sound theoretical base rather than on personal bias.
4d Rule
The 4d rule is applied when there are at least 4 observations excluding the outlier.It is preferable to have at least 10 observations, if not more.
Step 1 – Ignore the outlying value and find the arithmetic mean of the other values
Step 2 – Compute the average deviation of individual deviations from the mean after omitting the doubtful value
Average deviation = (d1+d2 +d3 +d4 +---------------+dn )/(n) = (Sigma (xi- bar x))/(n)
Multiply the average deviation by 4
Step 3– Calculate the difference between the suspect value and the mean from step one and represent this as z.
Where z = |bar x - x_d|
and xd is the doubtful value
Step 4 – if z is greater than 4 Ad reject the doubtful value otherwise it can be retained
Q-Test
The Q test offers another approach to rejection or selection of doubtful values.
The rejection quotient is defined as the ratio of the divergence of the doubtful value from its nearest neighbour when the values are arranged in a sequence. If the value of Q is greater than the Q value given in the table at the desired confidence level for a given number of observations the suspect value is rejected.
Step 1 – Arrange your observations in ascending or descending order. The lowest or highest values could be the doubtful values
Step 2 - Calculate the range, R= Highest – Lowest value
Step 3 - Find the difference between the doubtful value and its nearest neighbour and call this difference Y
Step 4 – Calculate rejection quotient Q_calculated= Y/R
**Step 5–**Look up the Q table for the given number of observations and term the value Q_table
Step 6 – If Q_calculated is greater than Q_table the suspect value is rejected
it can be appreciated that the solution does not lie in hiding doubtful results under the carpet but by applying statistical principles to arrive at the correct decision so that you will be able to justify yourself if called upon to do so.
On what basis should an analytical result be accepted or rejected?
Basic statistics, rather than personal bias, should be used to judge whether an outlying value should be included or rejected, giving the decision a sound theoretical foundation.
What is the 4d rule for rejecting outlying analytical results?
The 4d rule requires at least 4 observations excluding the outlier, preferably 10 or more. The doubtful value is ignored to calculate the mean of the remaining values, the average deviation from that mean is computed and multiplied by 4, and the doubtful value is rejected if the difference between it and the mean exceeds this figure.
What is the Q-test used for in analytical chemistry?
The Q-test is another statistical method for deciding whether to reject a doubtful value. It calculates a rejection quotient as the ratio of the gap between the doubtful value and its nearest neighbor to the overall range of the data, and rejects the value if this calculated Q exceeds the tabulated Q value for the given number of observations and confidence level.
How many observations are needed to apply the Q-test?
The Q-test requires arranging observations in ascending or descending order so the highest or lowest value, which is typically the doubtful one, can be compared against a Q table for the corresponding number of observations.
Does the number of observations affect how much an outlier matters?
Yes. In a large set of observations, a single outlying value has only a small effect on the mean, so the decision to include or reject it is less significant, whereas in a small set of observations the impact of that decision can be significant.
Is it acceptable to simply discard an unexpected analytical result?
No, the correct approach is not to hide doubtful results but to apply statistical principles such as the 4d rule or Q-test to reach a defensible decision that can be justified if questioned.