skbio.stats.distance.anosim#

skbio.stats.distance.anosim(distance_matrix, grouping, column=None, permutations=999)[source]#

Test for significant differences between groups using ANOSIM.

Analysis of Similarities (ANOSIM) is a non-parametric method that tests whether two or more groups of objects (e.g., samples) are significantly different based on a categorical factor. The ranks of the distances in the distance matrix are used to calculate an R statistic, which ranges between -1 (anti-grouping) to +1 (strong grouping), with an R value of 0 indicating random grouping.

Statistical significance is assessed via a permutation test. The assignment of objects to groups (grouping) is randomly permuted a number of times (controlled via permutations). An R statistic is computed for each permutation and the p-value is the proportion of permuted R statisics that are equal to or greater than the original (unpermuted) R statistic.

Parameters:
distance_matrixDistanceMatrix

Distance matrix containing distances between objects (e.g., distances between samples of microbial communities).

grouping1-D array_like or pandas.DataFrame

Vector indicating the assignment of objects to groups. For example, these could be strings or integers denoting which group an object belongs to. If grouping is 1-D array_like, it must be the same length and in the same order as the objects in distance_matrix. If grouping is a DataFrame, the column specified by column will be used as the grouping vector. The DataFrame must be indexed by the IDs in distance_matrix (i.e., the row labels must be distance matrix IDs), but the order of IDs between distance_matrix and the DataFrame need not be the same. All IDs in the distance matrix must be present in the DataFrame. Extra IDs in the DataFrame are allowed (they are ignored in the calculations).

columnstr, optional

Column name to use as the grouping vector if grouping is a DataFrame. Must be provided if grouping is a DataFrame. Cannot be provided if grouping is 1-D array_like.

permutationsint, optional

Number of permutations to use when assessing statistical significance. Must be greater than or equal to zero. If zero, statistical significance calculations will be skipped and the p-value will be np.nan.

Returns:
pandas.Series

Results of the statistical test, including test statistic and p-value.

See also

permanova

Notes

See [1] for the original method reference. The general algorithm and interface are similar to vegan::anosim, available in R’s vegan package [2].

The p-value will be np.nan if permutations is zero.

References

[1]

Clarke, KR. “Non-parametric multivariate analyses of changes in community structure.” Australian journal of ecology 18.1 (1993): 117-143.

Examples

Load a 4x4 distance matrix and grouping vector denoting 2 groups of objects:

>>> from skbio import DistanceMatrix
>>> dm = DistanceMatrix([[0, 1, 1, 4],
...                      [1, 0, 3, 2],
...                      [1, 3, 0, 3],
...                      [4, 2, 3, 0]],
...                     ['s1', 's2', 's3', 's4'])
>>> grouping = ['Group1', 'Group1', 'Group2', 'Group2']

Run ANOSIM using 99 permutations to calculate the p-value:

>>> import numpy as np
>>> # make output deterministic; not necessary for normal use
>>> np.random.seed(0)
>>> from skbio.stats.distance import anosim
>>> anosim(dm, grouping, permutations=99)
method name               ANOSIM
test statistic name            R
sample size                    4
number of groups               2
test statistic              0.25
p-value                     0.67
number of permutations        99
Name: ANOSIM results, dtype: object

The return value is a pandas.Series object containing the results of the statistical test.

To suppress calculation of the p-value and only obtain the R statistic, specify zero permutations:

>>> anosim(dm, grouping, permutations=0)
method name               ANOSIM
test statistic name            R
sample size                    4
number of groups               2
test statistic              0.25
p-value                      NaN
number of permutations         0
Name: ANOSIM results, dtype: object

You can also provide a pandas.DataFrame and a column denoting the grouping instead of a grouping vector. The following DataFrame’s Group column specifies the same grouping as the vector we used in the previous examples:

>>> # make output deterministic; not necessary for normal use
>>> np.random.seed(0)
>>> import pandas as pd
>>> df = pd.DataFrame.from_dict(
...     {'Group': {'s2': 'Group1', 's3': 'Group2', 's4': 'Group2',
...                's5': 'Group3', 's1': 'Group1'}})
>>> anosim(dm, df, column='Group', permutations=99)
method name               ANOSIM
test statistic name            R
sample size                    4
number of groups               2
test statistic              0.25
p-value                     0.67
number of permutations        99
Name: ANOSIM results, dtype: object

The results match the first example above.

Note that when providing a DataFrame, the ordering of rows and/or columns does not affect the grouping vector that is extracted. The DataFrame must be indexed by the distance matrix IDs (i.e., the row labels must be distance matrix IDs).

If IDs (rows) are present in the DataFrame but not in the distance matrix, they are ignored. The previous example’s s5 ID illustrates this behavior: note that even though the DataFrame had 5 objects, only 4 were used in the test (see the “Sample size” row in the results above to confirm this). Thus, the DataFrame can be a superset of the distance matrix IDs. Note that the reverse is not true: IDs in the distance matrix must be present in the DataFrame or an error will be raised.

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