Chauvenetís Criterion

 

Consider n measurements of a quantity are taken such that the sample population is large enough to form a Gaussian distribution. The distribution may then be used to compute the probability that a given reading will deviate a certain amount from the mean (usually not expected to be < 1/n). So if a probability for an observed deviation is actually less than 1/n then that point becomes suspicious.

 

A test has been developed to eliminate suspicious points:

 

Chauvenetís Criterion:A reading may be rejected if the probability of obtaining the particular deviation is less than 1/2n.

The following table lists values of the ratio of deviation to standard deviation for various values of n according to this criterion.

 

Number of Readings, n

Ratio of Maximum Acceptable Deviation to Standard Deviation, dmax /σ

3

1.38

4

1.54

5

1.65

6

1.73

7

1.80

10

1.96

15

2.13

25

2.33

50

2.57

100

2.81

300

3.14

500

3.29

1,000

3.48

 

Procedure:

1.      Calculate mean value and standard deviation using all data points.

2.      Compare deviations of individual points in accordance with information in previous table.

3.      Dubious points are eliminated.

4.      Calculate new mean and standard deviation.

 

Example:

The following readings are taken of a certain physical length.

 

Reading

x, cm

1

5.30

2

5.73

3

6.77

4

5.26

5

4.33

6

5.45

7

6.09

8

5.64

9

5.80

10

5.75

 

The best estimate of the standard deviation is given by

 


 


and results in 0.627 cm.

 

Reading

di /σ

1

0.499

2

0.187

3

1.845

4

0.563

5

2.046

6

0.260

7

0.761

8

0.043

9

0.314

10

0.219

 

Checking the Criterion table, we may eliminate point 5. The new mean is calculated and the new standard deviation becomes 0.4615 cm (26.5% reduction).

 

 

Ref: J.P. Holman, W.J. Gajda, Jr., Experimental Methods for Engineers, 5th Edition, McGraw-Hill, 1989.