DavidHartleyPearsonTest (FPScript)
Carries out a David-Hartley-Pearson outlier test. The test checks whether the highest or lowest value in the normally distributed sample passed belongs to the sample or not.
Syntax
DavidHartleyPearsonTest(Sample, ErrorProbability, Result)
The syntax of the DavidHartleyPearsonTest function consists of the following parts:
Part |
Description |
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Sample |
Contains the sample to be examined with at least 3 values and a maximum of 1000 values. Permitted data structures are data series und signal. All numeric data types are permitted. For complex data types the absolute value is formed. If the argument is a list, then the function is executed for each element of the list and the result is also a list. |
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ErrorProbability |
Specifies the error probability, on which the test is to be based, as a percentage. Here, the values 0.5, 1, 2.5, 5 and 10 % are permitted. Permitted data structures are scalar value. All numeric data types are permitted. The argument is transformed to the unit %. If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated. |
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Result |
Determines the result of the function. The argument Result can have the following values:
If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated. |
Remarks
The sample must originate from a normally distributed population.
The result is either an integral value, which represents the test result, or the sample cleaned of outliers with a 64-bit floating point value data type. The values recognized as being outliers are marked as void.
In the first case, the following values are possible:
Value |
Interpretation |
|---|---|
0 |
The hypothesis was rejected. The lowest or highest value is, with the error probability specified, an outlier. |
1 |
The hypothesis was accepted. The lowest and highest values are, with the error probability specified, not outliers. |
2 |
No result could be determined, since the sample size is outside the valid range. |
Available in
Option Enhanced Statistics
Examples
DavidHartleyPearsonTest({36, 37, 39, 39, 40, 40, 41, 41, 41,42, 44, 46}, 1 %, TEST_RESULT)
Results in 1s. The quotient from the difference between the largest and smallest value of the data series and the standard deviation is smaller than the quantile of the David-Hartley-Pearson test.
Q = R / s = (46 - 36) / Sqrt(Variance({36, 37, 39, 39, 40, 40, 41, 41, 41,42, 44, 46}) < 4.13 = Q12,0.99
Thus, neither the smallest nor the largest value is an outlier when the error probability is one percent.
See Also
References
[1] "Hartung, Joachim": "Statistik (Statistics), 9th Edition", page 344. "Oldenbourg Verlag GmbH, Munich",1993.ISBN 3-486-22055-1.
[2] "David, H.A., Hartley, H.O., Pearson, E.S.": "The distribution of the ratio, in a single normal sample, of range to standard deviation". In: "Biometrika, vol. 41", page 491. 1954.