Home : Outlier Detection
Q14221 - INFO: Outlier Detection

When calculating Control Limits for SPC, lab quality control outliers (values that are abnormally distant from the rest of the data) can be detected. Outliers will also be removed from the data set and the Mean, Standard Deviation, and mean +-2 and 3 standard deviations are recalculated and reported separately from the basic statistics. Detecting outliers to calculate future QC limits is recommended as standard deviations from data sets that include outliers may be misleading.

In both the QC Report and Variable Analysis Graphs, control limits can be calculated with and without the outliers removed.  When detecting and removing outliers you have the following options:

Off: Outliers will not be detected

T Test (Critical Value 5%): Tests each value using the Critical Value 5% table. Calculates a "Z" value for the high value in the set of data and compares it to the Critical Z value for the number of results (N in the table) from the table below. Z = (Mean - data value) / Standard Deviation. If the Z is above the Critical Z it is marked as an outlier and the test is repeated until no outliers exist.

N Critical Z N Critical Z
3 1.15 22 2.924
4 1.49 23 2.946
5 1.75 24 2.968
6 1.94 25 2.99
7 2.1 26 3.012
8 2.22 27 3.034
9 2.32 28 3.056
10 2.41 29 3.078
11 2.48 30 3.1
12 2.55 31-39 3.1+(((n-30)/10)*(3.24-3.1))
13 2.61 40 3.24
14 2.66 41-49 3.24+(((n-40)/10)*(3.34-3.24))
15 2.71 50 3.34
16 2.75 51-59 3.34+(((n-50)/10)*(3.41-3.34))
17 2.79 60 3.41
18 2.82 61-99 3.41+(((n-60)/10)*(3.6-3.41))
19 2.85 100 3.6
20 2.88 101-119 3.6+(((n-100)/10)*(3.66-3.6))
21 2.902 120 3.66
>120 3.7

T Test (Critical Value 1%): Tests each value using the Critical Value 1% table. Calculates a "Z" value for the high value in the set of data and compares it to the Critical Z value for the number of results (N in the table) from the table below. Z = (Mean - data value) / Standard Deviation. If the Z is above the Critical Z it is marked as an outlier and the test is repeated until no outliers exist.

N Critical Z N Critical Z
3 1.15 22 2.596
4 1.46 23 2.614
5 1.67 24 2.632
6 1.82 25 2.65
7 1.94 26 2.668
8 2.03 27 2.686
9 2.11 28 2.704
10 2.18 29 2.722
11 2.24 30 2.74
12 2.29 31-39 2.74 + (((n - 30) / 10) * (2.87 - 2.74))
13 2.33 40 2.87
14 2.37 41-49 2.87 + (((n - 40) / 10) * (2.96 - 2.87))
15 2.41 50 2.96
16 2.44 51-59 2.96 + (((n - 50) / 10) * (3.03 - 2.96))
17 2.47 60 3.03
18 2.5 61-99 3.03 + (((n - 60) / 10) * (3.21 - 3.03))
19 2.53 100 3.21
20 2.56 101-119 3.21 + (((n - 100) / 10) * (3.27 - 3.21))
21 2.578 120 3.27
>120 3.3

Grubbs Test: Tests each value against the "Grubbs" test for outliers. The Grubbs test calculates a "Z" value for the high value in the set of data and compares it to the Critical Z value from the table below. Z = (Mean - data value) / Standard Deviation. If the Z is above the Critical Z it is marked as an outlier and the Grubbs test is run again.

N Critical Z N Critical Z N Critical Z
3 1.15 20 2.71 37 3.00
4 1.48 21 2.73 38 3.01
5 1.71 22 2.76 39 3.03
6 1.89 23 2.78 40 3.04
7 2.02 24 2.80 50 3.13
8 2.13 25 2.82 60 3.20
9 2.21 26 2.84 70 3.26
10 2.29 27 2.86 80 3.31
11 2.34 28 2.88 90 3.35
12 2.41 29 2.89 100 3.38
13 2.46 30 2.91 110 3.42
14 2.51 31 2.92 120 3.44
15 2.55 32 2.94 130 3.47
16 2.59 33 2.95 140 3.49
17 2.62 34 2.97 >140 3.5
18 2.65 35 2.98
19 2.68 36 2.99

* Critical Z is interpolated (straight line) if N is not an exact match in the table above.

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Created on 6/20/2014 1:37 PM.
Last Modified on 6/23/2014 4:50 PM.
Last Modified by Scott Dorner.
Article has been viewed 2336 times.
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