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

### Options

`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 |

### Parameters

`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 |

### Description

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 (2*n* + 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.

Options: `PRINT`

, `METHOD`

, `TREATMENTS`

, `CONTROL`

, `NTIMES`

, `SEED`

.

Parameters: `DATA`

, `SUMRANKS`

, `RANKS`

.

### Action with `RESTRICT`

`DATA`

or `TREATMENTS`

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

### Reference

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

### See also

Procedures: `AMCOMPARISON`

, `AUMCOMPARISON`

, `AMDUNNETT`

, `CONFIDENCE`

, `VMCOMPARISON`

.

Commands for: Basic and nonparametric statistics.

### Example

CAPTION 'STEEL example',\ !t('Data from Steel (1959)',\ 'Binnet IQ scores of 3-year old female, white, private patients');\ STYLE=meta,plain FACTOR [NVALUES=24; LABELS=!t(Normal,Anoxic,'Rh negative',Premature);\ VALUES=(1...4)6] Treatment VARIATE [NVALUES=24] IQ READ IQ 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