Rejection of Discordant Data

It occasionally happens in making multiple measurements that one value differs from the rest considerably more than they differ from one another. Should the discordant value be rejected before an average is taken This question provides one of the most severe tests of yom scientific objectivity, for you may (indeed, you should) reject any measurement, whether concordant or discordant, if there is a valid reason to believe that it is defective. 

Q Test. When one in a series of 3 to 10 measurements appears to deviate from the mean by more than seems reasonable, calcnlate the quantity Q, defined by 

Compare this value of Q with the critical value in Table 1 corresponding to the number of observations in the series. If Q is eqnal to or larger than Q the suspect measurement shonld be rejected. If Q is less than Q this measnrement mnst be retained. 

EXAMPLE. Five determinations of the baseline reading of a spectrophotometer at a standardizing wavelength were 0.32,0.38,0.21, 0.35, and 0.34 absorbance units. May the 0.21 be discarded  

From Table 1, the critical value for jV = 5 is 0.64. The value of Q is higher, hence the 0.21 value may be discarded with 90 percent confidence. 

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We now assume that the least-squares refinement has converged satisfactorily, that any necessary rejection of discordant data has taken place before the final cycles were carried out, and that statistical tests on the weighted residuals have given reassuring results. It is now appropriate to estimate the uncertainties in the determined values of the adjustable parameters a,.f... 

Reject any obviously bad points (see Rejection of Discordant Data). 

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