What is the basis of selection or rejection of analytical results?

What is the basis of selection or rejection of analytical results?
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 =\( \frac{d1+d2 +d3 +d4 +—————+dn } {n}\) = \(\frac{\Sigma  (xi- \bar x)}{n}\)

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


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 \(Q_c_a_l_c_u_l_a_t_e_d\)= Y/R

Step 5–Look up the Q table for the given number of observations and term the value \(Q_t_a_b_l_e\)

Step 6 – If \(Q_c_a_l_c_u_l_a_t_e_d\) is greater than \(Q_t_a_b_l_e\) 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.

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  1. Very interesting article, quite easy to understand.
    One question: as there are several and different denominations, where can we find Q table?

    1. Hi Maria,
      Good to note that you liked the article.Q-Test tables are generally available in standard analytical texts and can be specificfor 90%, 95% and 99% confidence levels. These tables can also be accessed on the internet.


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