
DAVID TESTName:
The test statistic is
with \( r \) and \( s \) denoting the sample range and sample standard deviation, respectively. Dataplot supports several methods for deterining the critical values for this test.
To specify the method used to compute the critical value, enter one of the following commands (the default is ASTM)
SET DAVID TEST CRITICAL VALUES DAVID SET DAVID TEST CRITICAL VALUES FORMULA SET DAVID TEST CRITICAL VALUES SIMULATION This test is included in the ASTM E178 standard for outliers.
where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of up to k response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs the David test on <y1>, then on <y2>, and so on. Up to 30 response variables may be specified. Note that the syntax
is supported. This is equivalent to
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> is a list of up to k groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs a crosstabulation of <x1> ... <xk> and performs a David test for each unique combination of crosstabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be a total of 6 David tests performed. Up to six groupid variables can be specified. Note that the syntax
is supported. This is equivalent to
MULTIPLE DAVID TEST Y1 Y2 Y3 REPLICATED DAVID TEST Y X1 X2 DAVID TEST Y1 SUBSET TAG > 2
The STATCDF and PVALUE are only saved when the simulation method is used to obtain critical values. If the ASTM method is used to obtain critical values, the CUTOFF80 and CUTOF975 values are not saved. When the DAVID method is used to obtain critical values, the CUTOFF80 value is not saved. If the MULTIPLE or REPLICATED option is used, these values will be written to the file "dpst1f.dat" instead.
LET A = DAVID TEST CDF Y LET A = DAVID TEST PVALUE Y LET A = DAVID TEST MINIMUM INDEX Y LET A = DAVID TEST MAXIMUM INDEX Y
LET ALPHA = <value> The DAVID TEST, DAVID TEST CDF, and DAVID TEST PVALUE return the values of the test statistic, the cdf of the test statistic and the pvalue of the test statistic, respectively. For the DAVID TEST CDF and DAVID TEST PVALUE commands, the simulation method will be used. Otherwise, the method specified by the SET DAVID TEST CRITICAL VALUE command will be used. The DAVID TEST MINIMUM INDEX and DAVID TEST MAXIMUM INDEX return the row index of the minimum and maximum values of the response variable, respectively. The DAVID TEST CRITICAL VALUE returns the critical value for the specified value of ALPHA. If ALPHA is not specified, it will be set to 0.05. Note that if the ASTM or DAVID methods are specified for the critical values, only a few select values for alpha are supported (0.01, 0.05 and 0.10 for ASTM and 0.005, 0.01, 0.025, 0.05 and 0.10 for DAVID). In addition to the above LET command, builtin statistics are supported for about 25 different commands (enter HELP STATISTICS for details).
E178  16A (2016), "Standard Practice for Dealing with Outlying Observations", ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 194282959, USA.
. Step 1: Read the data  example from ASTM E178 standard . read y 1.40 0.44 0.30 0.24 0.22 0.13 0.05 0.06 0.10 0.18 0.20 0.39 0.48 0.63 1.01 end of data . . Step 2: Perform the DAVID TEST . set write decimals 3 set david test critical values astm david test y set david test critical values david david test y set david test critical values formula david test y set david test critical values simulation david test yThe following output is generated THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO ASTM David, Hartley, Pearson Test for Outliers: Simultaneous Test for Minimum and Maximum (Assumption: Normality) Response Variable: Y H0: The minimum and maximum are not both outliers Ha: Both the minimum and maximum are outliers Potential minimum outlier value tested: 1.400 Potential maximum outlier value tested: 1.010 Summary Statistics: Number of Observations: 15 Sample Minimum: 1.400 ID for Sample Minimum: 1 Sample Maximum: 1.010 ID for Sample Maximum: 15 Sample Mean: 0.018 Sample SD: 0.551 Sample Range: 2.410 David Test Statistic Value: 4.374 Conclusions (Upper 1Tailed Test)  Alpha CDF Statistic Critical Value Conclusion  10% 90% 4.374 4.025 Reject H0 5% 95% 4.374 4.171 Reject H0 1% 99% 4.374 4.435 Accept H0 Critical Values Based on ASTM E178 Tables THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO DAVI David, Hartley, Pearson Test for Outliers: Simultaneous Test for Minimum and Maximum (Assumption: Normality) Response Variable: Y H0: The minimum and maximum are not both outliers Ha: Both the minimum and maximum are outliers Potential minimum outlier value tested: 1.400 Potential maximum outlier value tested: 1.010 Summary Statistics: Number of Observations: 15 Sample Minimum: 1.400 ID for Sample Minimum: 1 Sample Maximum: 1.010 ID for Sample Maximum: 15 Sample Mean: 0.018 Sample SD: 0.551 Sample Range: 2.410 David Test Statistic Value: 4.374 Conclusions (Upper 1Tailed Test)  Alpha CDF Statistic Critical Value Conclusion  10% 90% 4.374 4.020 Reject H0 5% 95% 4.374 4.170 Reject H0 2.5% 97.5% 4.374 4.290 Reject H0 1% 99% 4.374 4.430 Accept H0 0.5% 99.5% 4.374 4.530 Accept H0 Critical Values Based on David Tables THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO FORM David, Hartley, Pearson Test for Outliers: Simultaneous Test for Minimum and Maximum (Assumption: Normality) Response Variable: Y H0: The minimum and maximum are not both outliers Ha: Both the minimum and maximum are outliers Potential minimum outlier value tested: 1.400 Potential maximum outlier value tested: 1.010 Summary Statistics: Number of Observations: 15 Sample Minimum: 1.400 ID for Sample Minimum: 1 Sample Maximum: 1.010 ID for Sample Maximum: 15 Sample Mean: 0.018 Sample SD: 0.551 Sample Range: 2.410 David Test Statistic Value: 4.374 Conclusions (Upper 1Tailed Test)  Alpha CDF Statistic Critical Value Conclusion  20% 80% 4.374 3.875 Reject H0 10% 90% 4.374 4.034 Reject H0 5% 95% 4.374 4.173 Reject H0 2.5% 97.5% 4.374 4.295 Reject H0 1% 99% 4.374 4.435 Accept H0 0.5% 99.5% 4.374 4.527 Accept H0 Critical Values Based on Formula THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO SIMU David, Hartley, Pearson Test for Outliers: Simultaneous Test for Minimum and Maximum (Assumption: Normality) Response Variable: Y H0: The minimum and maximum are not both outliers Ha: Both the minimum and maximum are outliers Potential minimum outlier value tested: 1.400 Potential maximum outlier value tested: 1.010 Summary Statistics: Number of Observations: 15 Sample Minimum: 1.400 ID for Sample Minimum: 1 Sample Maximum: 1.010 ID for Sample Maximum: 15 Sample Mean: 0.018 Sample SD: 0.551 Sample Range: 2.410 David Test Statistic Value: 4.374 CDF Value: 0.986 PValue 0.014 Conclusions (Upper 1Tailed Test)  Alpha CDF Statistic Critical Value Conclusion  20% 80% 4.374 3.842 Reject H0 10% 90% 4.374 4.021 Reject H0 5% 95% 4.374 4.166 Reject H0 2.5% 97.5% 4.374 4.296 Reject H0 1% 99% 4.374 4.428 Accept H0 0.5% 99.5% 4.374 4.523 Accept H0 Critical Values Based on 50,000 Simulations  
Date created: 01/22/2020 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 