Chauvenet’s
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:
Chauvenet’s
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, d_{max }/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

d_{i }/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, 5^{th}
Edition, McGrawHill, 1989.