Analysis of similarities (ANOSIM) is a
non-parametric statistical test widely used in the field of
ecology. The test was first suggested by K. R. Clarke
as an
ANOVA-like test, where instead of operating on
raw data, operates on a ranked dissimilarit
matrix
Given a matrix of rank
dissimilarities between a set of samples, each belonging to a single site (e.g. a single
treatment group), the ANOSIM tests whether we can reject the
null hypothesis that the similarity between sites is greater than or equal to the
similarity within each site.
The test statistic ''R'' is calculated in the following way:
:
where
B is the average of rank similarities of pairs of samples (or replicates) originating from different sites,
W is the average of rank similarity of pairs among
replicates within sites, and ''M'' = ''n''(''n'' − 1)/2 where ''n'' is the number of samples.
The test statistic ''R'' is constrained between the values −1 to 1, where
positive numbers suggest more similarity within sites and values close to zero represent no difference between sites and within sites similarities. Negative ''R'' values suggest more similarity between sites than within sites and may raise the possibility of wrong assignment of samples to sites.
For the purpose of
hypothesis testing, where the null hypothesis is that the similarities within sites are smaller or equal to the similarities between sites, the ''R'' statistic is usually compared to a set of ''R′'' values that are achieved by means of randomly shuffling site labels between the samples and calculating the resulting ''R′'', repeated many times. The percent of times that the actual ''R'' surpassed the
permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
s derived ''R′'' values is the p-value for the actual ''R'' statistic.
Ranking of dissimilarity in ANOSIM and
NMDS (non-metric multidimensional scaling) go hand in hand.
Combining both methods complement visualisation of group differences along with
significance testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis.
Hypothesis testing allows us to make probabilistic statements about population parameters.
...
.
ANOSIM is implemented in several statistical software including PRIMER, the R Vegan package
and PAST.
References
{{reflist, 2
External links
* http://www.pisces-conservation.com/caphelp/index.html?analysisofsimilarity(anosim.html
* https://bizfluent.com/about-5475541-similarities-between-swot-pest-analysis.html
Ecology
Statistical tests