Performs an analysis of similarities i.e. *ANOSIM* (D.A. Murray).

### Options

`PRINT` = string token |
Controls printed output (`test` ); default `test` |
---|---|

`PLOT` = string token |
Type of plot (`boxplot` , `histogram` ); default `hist` |

`NTIMES` = scalar |
Number of permutations to make; default 999 |

`BLOCKS` = factor |
Factor specifying groups for a stratified test; default `*` i.e. none |

`SEED` = scalar |
Seed for the random number generator used to make the permutations; default 0 continues from the previous generation or (if none) initializes the seed automatically |

### Parameters

`DATA` = symmetric matrices |
Similarity matrix |
---|---|

`GROUPS` = factors |
Specify the different groups for each matrix |

`STATISTIC` = scalars |
Save the R statistics |

`PROBABILITY` = scalars |
Save the probabilities |

### Description

Analysis of similarities (*ANOSIM*) is a nonparametric method to test whether there is a significant difference between two or more groups of sampling units (Clarke 1993). The method performs a permutation test based on the ranks of measures of similarity between sampling units. The data should be supplied as a similarity matrix using the `DATA`

parameter. The `GROUPS`

parameter specifies a factor containing the groups for each corresponding row of the similarity matrix.

The *ANOSIM* statistic *R* is calculated by the difference of the between-group (*r _{b}*) and within-group (

*r*) mean rank similarities:

_{w}*R* = (mean(*r _{b}*) – mean(

*r*)) / (

_{w}*n*× (

*n*– 1) / 4)

The denominator is chosen so the *R* lies in the range (-1, 1) where 0 represents no difference between the groups. The similarites are ranked where a rank of 1 corresponds to the highest similarity.

The statistical significance of the *R* statistic is assessed by a permutation test. `ECANOSIM`

performs 999 random permutations (made using a default seed), and calculates the *R* statistic for each permutation. The probability for the *R* statistic is then determined from its distribution over the randomly permuted datasets. The `NTIMES`

option of `ECANOSIM`

allows you to request another number of permutations, and the `SEED`

option allows you to specify another seed. For designs with no blocking `ECANOSIM`

checks whether `NTIMES`

is greater than the number of possible permutations available for the data set. If so, `ECANOSIM`

does an exact test instead, which uses each possible permutation once.

The `histogram`

setting of the `PLOT`

option can be used to produce a distribution of the *R* values. *ANOSIM* assumes under the null hypothesis that distances within groups are smaller than those between groups, and that the ranked dissimilarities within groups have equal median and range. The `boxplot`

setting for the `PLOT`

option can be used to help check these assumptions.

The *R* statistic can be saved using the `STATISTIC`

parameter, and the probability can be saved using the `PROBABILITY`

parameter.

The `PRINT`

option controls printed output, with a setting:

`test` |
to print the R statistic and probability. |
---|

Options: `PRINT`

, `PLOT`

, `NTIMES`

, `BLOCKS`

, `SEED`

.

Parameters: `DATA`

, `GROUPS`

, `STATISTIC`

, `PROBABILITY`

.

### Method

The R statistic is calculated by:

*R* = (mean(*r _{b}*) – mean(

*r*)) / (

_{w}*n*× (

*n*– 1) / 4)

where mean(*r _{w}*) is the average of all rank similarities among replicates within sites, mean(

*r*) is the average of rank similarities from all pairs of replicates between sites and

_{b}*n*is total number of samples.

### Action with `RESTRICT`

The data must not be restricted.

### Reference

Clarke K,R. (1993). Non-parametric multivariate analyses of changes in community structure. *Australian Journal of Biology*, 18, 117-143.

### See also

Procedure: `MANTEL`

.

Commands for Ecological data.

### Example

CAPTION 'ECANOSIM Example'; style=meta FACTOR [LEVELS=5; VALUES=1,1,1,2,2,2,3,3,3,4,5,5,5,5] groups VARIATE [NVALUES=14] data[1...5]; VALUES=!(5(1),9(0)),\ !(8(1),4(0),1,0),!(0,4(1),0,4(1),0,0,1,0),\ !(0,5(1),0,3(1),4(0)),!(3(0),3(1),0,1,1,0,4(1)) FSIMILARITY [SIMILARITY=sim] data[]; TEST=jaccard ECANOSIM [SEED=10416] sim; GROUPS=groups