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STEEL procedure

Performs Steel’s many-one rank test (R.W. Payne).


PRINT = string token Controls printed output (description, sumranks, critical, permutationtest); default desc, sumr, crit
METHOD = string token Form of the alternative hypothesis (twosided, greaterthan, lessthan); default twos
TREATMENTS = factor Defines the treatments
CONTROL = scalar or text Treatment level corresponding to the control; default takes the reference level of TREATMENTS
NTIMES = scalar Number of permutations for the permutation test; default 999
SEED = scalar Seed to use to generate the random numbers for the permutation test; default 0


DATA = variates Data values for the tests
SUMRANKS = tables Saves the sum of the ranks within the treatments from each test
RANKS = variates Saves the ranks of the data values for each test


Steel’s test (Steel 1959) is a multiple-comparison test for comparing several treatments with a control treatment. The data are assumed to come from a one-way classification where all the treatments (and the control) have equal replication. The data values are specified, in a variate, using the DATA parameter. The TREATMENTS option species a factor to indicate the allocation of data values to treatments. The CONTROL option indicates which level of the TREATMENTS factor is the control; if this is not set, the reference level of TREATMENTS is used.

The METHOD option defines the type of test that is done. By default STEEL does a two-sided test, so the test is against the alternative hypothesis that the treatments may be either less than or greater than the control. If you set METHOD=lowerthan, STEEL does a one-sided test of the null hypothesis that the treatment values are not lower than the control. Alternatively, you can set METHOD=greaterthan, to do a one-sided test of the null hypothesis that the treatment values are not greater than the control.

The test operates by comparing the data values from each treatment in turn with the control. The comparison is made by pooling the data values from the treatment and control, forming their ranks, and calculating the sum of the ranks for the treatment data values. For METHOD=greaterthan, the test statistic for each treatment is simply the sum of the ranks for each treatment. For METHOD=lessthan, each rank sum must be subtracted from the total sum of ranks (2n + 1) × n, where n is the replication of the treatments. For METHOD=twosided, the statistic is the minimum of the greaterthan and the lessthan statistics.

The PRINT option controls printed output, with settings:

    description description of the data and test;
    sumranks the test statistics (sums of ranks for each treatment);
    critical critical value as provided by Steel (1959);
    permutationtest uses a random permutation test to forms critical values and the probability that any treatment differs from control (according to the test specified by METHOD).

By default these are all produced.

By default, when PRINT=perm, STEEL makes 999 random allocations of the data to the treatment and control groups (using a default seed), and determines critical values for the test from the distribution of the minimum rank sum over these randomly generated datasets. The NTIMES option allows you to request another number of allocations, and the SEED option allows you to specify another seed. STEEL checks whether NTIMES is greater than the number of possible ways in which the data values can be allocated. If so, it does an exact test instead, which takes each possible allocation once. The results should be more reliable than Steel’s critical values, which are based on a multivariate Normal approximation.

The rank sums can be saved using the SUMRANKS parameter, and the ranks of the individual treatment data values can be saved using the RANKS parameter.



Action with RESTRICT

DATA or TREATMENTS can be restricted to analyse a subset of the data values.


Steel, R.G.D. (1959). A multiple comparison rank sum test: treatments versus control. Biometrics, 15, 560-572.

See also


Commands for: Basic and nonparametric statistics.


CAPTION 'STEEL example',\
        !t('Data from Steel (1959)',\
        'Binnet IQ scores of 3-year old female, white, private patients');\
FACTOR  [NVALUES=24; LABELS=!t(Normal,Anoxic,'Rh negative',Premature);\
        VALUES=(1...4)6] Treatment
103 119  89  92
111 100 132 114
136  97  86  86
106  89 114 119
122 112 114 131
114  86 125  94 :
STEEL   [METHOD=less; TREATMENTS=Treatment; CONTROL='Normal'; SEED=574750] IQ
Updated on June 18, 2019

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