6.2.2. Charlier criterion
It is advisable to apply the Charlier criterion only for series of measurements, in which n & gt; 20. If the number of measurement results n & gt; 20, then by Bernoulli's theorem the number of results exceeding the absolute value of Kmax will be equal to [I-Ф (КШ)], where Ф (КШШ) is the value of the normalized Laplace function for Z = Кш.
If one result is doubtful in a series of observations, then
From here) = -.
Critical values of the Charlier criterion can be determined by the formula
Using Charlier's criterion, discard the result, whose value exceeds modulo Кшхх
The order of detection and exclusion of gross errors and misses using the Charlier criterion is reduced to the following:
- the average value of the measurement results is determined
- the estimate of the mean square deviation φ is determined from
- the calculated (critical) value of the Charlier criterion is determined by the equation (6.8),
- the absolute value of the difference between the doubtful
result, that is, -X;
- compare the values of
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if 1 * ^, - X & gt; then the result is discarded as containing a gross error;
if xc & lt; tn - X & lt; 5 (x) АГш, the result does not contain a gross error.
6.2.3. Chauvenais criterion
The Chauvenais criterion is based on the same assumptions as the Charlier criterion. It can be used if the number of measurement results is less than 20.
The critical area for this criterion is determined by the inequality
Results, the values of which in the series of n observations exceed the value of 2mot in modulus, are discarded as misses. Exception results are performed in this order.
First, discard one result with the largest deviation from x from the module and count the ah again. If, in this case too, the Chauvenet criterion is violated, then the next one with the greatest deviation, etc., is excluded
The critical value of the Chauvenet criterion can be determined by the formula
(for 2 & lt; n <20).
The order of detection and exclusion of gross errors and misses using the Chauvenais criterion is similar to the Charlier test.
If -X & gt; 5 & lt; x) АГш, the result is discarded as containing a gross error;
if Isoyn - X & lt; the result does not contain a gross error.
6.2.4. Dixon Criterion
Dixon's criterion (Kd) is a convenient and powerful enough criterion. To use the Dixon test, the measurement results are placed in a variational increasing series, & lt; x, & lt; ... & lt; x & quot;.
Dixon's criterion is determined by the formula
Critical area for this criterion
The values of 2т (с (ду п) are calculated by the formulas
(where 4 & lt; n & lt; 30).
The order of detection and exclusion of gross errors and misses using Dixon's criterion is as follows:
- the values of the measurement results are sorted in ascending order;
- the calculated (critical) value of the Dickson test is determined by the formulas (6.13) - (6.16) for the accepted significance level
h-t ^ M *;);
- the value of the Dixon criterion (Kd) is determined by the formula (6.11);
- the values of AGD and n) are compared:
if the & amp; gt; 2, nks (& lt; 7, i), the result is discarded as containing a gross error;
if AGD & lt; (D, n), then the result does not contain a rough error (a miss) with probability P = I - a.
If there is reason to believe that the two largest (or two least) results are "misses", then you can use a method based on estimating the maximum differences in the results of the measurement.
To do this, you must arrange the results in ascending order. The minimum value in the series of observations will be ya and the maximum value is ynV where n is the number of measurement results;
- if the dubious result is ynU then calculate the ratio
- if the doubtful result is yy, then the ratio
The critical value of the criterion is determined by a formula that simultaneously takes into account the number of observations n and the significance level n = 0.05 (/> = 0.95), q = 0.01 (/> = 0.99):
where х = In & quot ;, у = щ.
The application of the criteria listed above requires consideration of measurement conditions. In case of doubt, you should try to perform additional measurements (if possible) and then use one or another criterion.
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