
TIETJENMOORE TESTName:
It is important to note that the TietjenMoore test requires that the suspected number of outliers be specified exactly. If this is not known, it is recommended that the generalized extreme studentized deviate test be used instead (this test only requires an upper bound on the number of suspected outliers). More formally, the TietjenMoore test can be defined as follows.
It is recommended that formal outlier tests be complemented with graphical methods. For example, a normal probability plot can be used to determine if the normality assumption is reasonable and also to determine an appropriate value for k.
where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax checks for outliers in both tails.
and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax checks the minimum values for outliers.
where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax checks the maximum values for outliers.
<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 can also be used with the MINIMUM and MAXIMUM version
of the tests. This syntax performs a TietjenMoore test on 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 can also be used with the MINIMUM and MAXIMUM version of the tests. This syntax peforms a crosstabulation of <x1> ... <xk> and performs a TietjenMoore 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 TietjenMoore tests performed. Up to six groupid variables can be specified. Note that the syntax
is supported. This is equivalent to
TIETJENMOORE TEST Y1 LABID TIETJENMOORE MULTIPLE TEST Y1 Y2 Y3 TIETJENMOORE REPLICATED TEST Y X1 X2 TIETJENMOORE TEST Y1 SUBSET TAG > 2 TIETJENMOORE MINIMUM TEST Y1 TIETJENMOORE MAXIMUM TEST Y1
Masking can occur when we specify too few outliers in the test. For example, if we are testing for a single outlier when there are in fact two (or more) outliers, these additional outliers may influence the value of the test statistic enough so that no points are declared as outliers. On the other hand, swamping can occur when we specify too many outliers in the test. For example, if we are testing for two outliers when there is in fact only a single outlier, both points may be declared outliers. The possibility of masking and swamping are an important reason why it is useful to complement formal outlier tests with graphical methods. Graphics can often help identify cases where masking or swamping may be an issue. Also, masking is one reason that trying to apply a single outlier test sequentially can fail. If there are multiple outliers, masking may cause the outlier test for the first outlier to return a conclusion of no outliers (and so the testing for any additional outliers is not done). The TietjenMoore test is used to check for exactly k outliers. If k is not specified correctly, the results of the TietjenMoore test can be distorted. If determining k is not obvious, then the generalized extreme studentized deviate tests may be preferred since this test only requires that an upper bound on the suspected number of outliers be specified.
If the MULTIPLE or REPLICATED option is used, these values will be written to the file "dpst1f.dat" instead.
LET A = TIETJENMOORE MINIMUM Y LET A = TIETJENMOORE MAXIMUM Y In addition to the above LET command, builtin statistics are supported for 20+ different commands (enter HELP STATISTICS for details).
REPLICATION TIETJEN MOORE is a synonym for TIETJEN MOORE REPLICATION
. Following example from TietjenMoore paper 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 . . First generate a normal probability plot . LABEL CASE ASIS TITLE CASE ASIS TITLE OFFSET 5 . Y1LABEL Data X1LABEL Theoretical TITLE Normal Probability Plot of SemiDiameters of Venus LINE BLANK CHAR CIRCLE CHAR FILL ON LET H = 1.2 LET W = H*0.75 CHAR HW H W . NORMAL PROBABILITY PLOT Y . . Now perform the TietjenMoore test . SET WRITE DECIMALS 5 LET NOUTLIER = 2 TIETJENMOORE YThe following output is generated
TietjenMoore Test for Multiple Outliers: TwoSided Case (Assumption: Normality) Response Variable: Y H0: There are no outliers Ha: The 2 most extreme points are outliers Potential Outlier Value Tested: 1.39999 Potential Outlier Value Tested: 0.06000 Summary Statistics: Number of Observations: 15 Sample Minimum: 1.39999 Sample Maximum: 1.01000 Sample Mean: 0.01800 Sample SD: 0.55094 TietjenMoore Test Statistic Value: 0.29199 CDF Value: 0.96560 PValue 0.03440 Percent Points of the Reference Distribution  Percent Point Value  0.0 = 0.064 1.0 = 0.237 2.5 = 0.277 5.0 = 0.315 10.0 = 0.362 25.0 = 0.435 50.0 = 0.508 100.0 = 0.755 Conclusions (Lower 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 10% 0.362 Reject H0 5% 5% 0.315 Reject H0 2.5% 2.5% 0.277 Accept H0 1% 1% 0.237 Accept H0 *Critical Values Based on 10000 Monte Carlo Simulations  
Date created: 09/09/2010 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 