Statistics

See Also

Statistics functions are implemented as part of SampleCollection. For more information, see SampleCollection.

Tests

aitchison_distance

SampleCollection.aitchison_distance(metric: Metric = auto, rank: Rank = auto) → skbio.stats.distance.DistanceMatrix

Calculate the Aitchison distance between samples.

Aitchison distance is the Euclidean distance between centre logratio-normalized samples (abundances). As this requires log-transforms, we first need to ‘estimate’ zeros in the data; i.e. replace zeros with small, positive values, while maintaining a constant sum to 1.

Parameters

metricMetric, optional

The taxonomic abundance metric to use. See Metric for definitions.

rankRank, optional

Analysis will be restricted to abundances of taxa at the specified level. See Rank for details.

Returns

skbio.stats.distance.DistanceMatrix, a distance matrix.

alpha_diversity

SampleCollection.alpha_diversity(metric: Metric = auto, rank=auto, diversity_metric: AlphaDiversityMetric = shannon) → pd.DataFrame

Calculate the diversity within a community.

Parameters

rankRank, optional

Analysis will be restricted to abundances of taxa at the specified level. See Rank for details.

metric: Metric, optional

The taxonomic abundance metric to use. See Metric for definitions.

diversity_metricAlphaDiversityMetric

Function to use when calculating the distance between two samples.

Returns

pandas.DataFrame, a distance matrix.

alpha_diversity_stats

SampleCollection.alpha_diversity_stats(*, group_by: str | tuple[str, ...] | list[str], paired_by: str | tuple[str, ...] | list[str] | None = None, metric: Metric = auto, test: AlphaDiversityStatsTest = auto, diversity_metric: AlphaDiversityMetric = shannon, rank: Rank = auto, alpha: float = 0.05) → AlphaDiversityStatsResults

Perform a test for significant differences between groups of alpha diversity values.

The following tests are supported:

  • Wilcoxon (2 groups, paired data)

  • Mann-Whitney U (2 groups, unpaired data)

  • Kruskal-Wallis with optional posthoc Dunn test (>=2 groups, unpaired data)

Parameters

group_bystr or tuple of str or list of str

Metadata variable to group samples by. At least two groups are required. If group_by is a tuple or list, field values are joined with an underscore character (“_”).

paired_bystr or tuple of str or list of str, optional

Metadata variable to pair samples in each group. May only be used with test=”wilcoxon”. If paired_by is a tuple or list, field values are joined with an underscore character (“_”).

testAlphaDiversityStatsTest, optional

Stats test to perform. If ‘auto’, ‘mannwhitneyu’ will be chosen if there are two groups of unpaired data. ‘wilcoxon’ will be chosen if there are two groups and paired_by is specified. ‘kruskal’ will be chosen if there are more than 2 groups.

rankRank, optional

Analysis will be restricted to abundances of taxa at the specified level. See Rank for details.

metric: Metric, optional

The taxonomic abundance metric to use. See Metric for definitions.

diversity_metricAlphaDiversityMetric

Function to use when calculating the distance between two samples.

alphafloat, optional

Threshold to determine statistical significance when test=”kruskal” (e.g. p < alpha). Must be between 0 and 1 (exclusive). If the Kruskal-Wallis p-value is significant and there are more than two groups, a posthoc Dunn test is performed.

Returns

AlphaDiversityStatsResults

See Also

scipy.stats.wilcoxon scipy.stats.mannwhitneyu scipy.stats.kruskal scikit_posthocs.posthoc_dunn

beta_diversity

SampleCollection.beta_diversity(metric: Metric = auto, rank: Rank = auto, diversity_metric: BetaDiversityMetric = braycurtis) → skbio.stats.distance.DistanceMatrix

Calculate the diversity between two communities.

Parameters

rankRank, optional

Analysis will be restricted to abundances of taxa at the specified level. See Rank for details.

metric: Metric, optional

The taxonomic abundance metric to use. See Metric for definitions.

diversity_metricBetaDiversityMetric

Function to use when calculating the distance between two samples.

Returns

skbio.stats.distance.DistanceMatrix, a distance matrix.

beta_diversity_stats

SampleCollection.beta_diversity_stats(*, group_by: str | tuple[str, ...] | list[str], metric: Metric = auto, diversity_metric: BetaDiversityMetric = braycurtis, rank: Rank = auto, alpha: float = 0.05, num_permutations: int = 999) → BetaDiversityStatsResults

Test for significant differences between groups of samples based on their distances.

Beta diversity distances between samples are computed and a PERMANOVA test is performed to assess whether there are significant differences between groups of samples. Posthoc pairwise PERMANOVA tests are performed if the global test is found to be statistically significant and there are more than two groups.

Parameters

group_bystr or tuple of str or list of str

Metadata variable to group samples by. At least two groups are required. If group_by is a tuple or list, field values are joined with an underscore character (“_”).

metric: Metric, optional

The taxonomic abundance metric to use. See Metric for definitions.

diversity_metricBetaDiversityMetric

Function to use when calculating the distance between two samples.

rankRank, optional

Analysis will be restricted to abundances of taxa at the specified level. See Rank for details.

alphafloat, optional

Threshold to determine statistical significance (e.g. p < alpha). Must be between 0 and 1 (exclusive). If the p-value is significant and there are more than two groups, posthoc pairwise PERMANOVA tests are performed.

num_permutationsint, optional

Number of permutations to use when computing the p-value.

Returns

BetaDiversityStatsResults

See Also

skbio.stats.distance.permanova scipy.stats.false_discovery_control

unifrac

SampleCollection.unifrac(metric: Metric = auto, rank: Rank = auto, weighted: bool = True)

Calculate the UniFrac beta diversity metric.

UniFrac takes into account the relatedness of community members. Weighted UniFrac considers abundances, unweighted UniFrac considers presence.

Parameters

metricMetric, optional

The taxonomic abundance metric to use. See Metric for definitions.

rankRank, optional

Analysis will be restricted to abundances of taxa at the specified level. See Rank for details.

weightedbool

Calculate the weighted (True) or unweighted (False) distance metric.

Returns

skbio.stats.distance.DistanceMatrix, a distance matrix.

Results

AlphaDiversityStatsResults

class onecodex.stats.AlphaDiversityStatsResults(test: AlphaDiversityStatsTest, statistic: float, pvalue: float, sample_size: int, group_by_variable: str, groups: set[str], paired_by_variable: str | None = None, posthoc: PosthocResults | None = None)

A dataclass for storing the results of an alpha diversity stats test.

  • test: stats test that was performed

  • statistic: computed test statistic (e.g. U statistic if test=”mannwhitneyu”)

  • pvalue: computed p-value

  • sample_size: number of samples used in the test after filtering

  • group_by_variable: name of the variable used to group samples by

  • groups: names of the groups defined by group_by_variable

  • paired_by_variable: name of the variable used to pair samples by (if the data were

paired) - posthoc: PosthocResults

BetaDiversityStatsResults

class onecodex.stats.BetaDiversityStatsResults(test: BetaDiversityStatsTest, statistic: float, pvalue: float, num_permutations: int, sample_size: int, group_by_variable: str, groups: set[str], posthoc: PosthocResults | None = None)

A dataclass for storing the results of a beta diversity test.

  • test: stats test that was performed

  • statistic: PERMANOVA pseudo-F test statistic

  • pvalue: p-value based on num_permutations

  • num_permutations: number of permutations used to compute pvalue

  • sample_size: number of samples used in the test after filtering

  • group_by_variable: name of the variable used to group samples by

  • groups: names of the groups defined by group_by_variable

  • posthoc: PosthocResults

PosthocResults

class onecodex.stats.PosthocResults(adjusted_pvalues: pd.DataFrame, pvalues: pd.DataFrame | None = None, statistics: pd.DataFrame | None = None)

A dataclass for storing results from the post-host correction of a statistical test.

  • statistics: pd.DataFrame containing pairwise PERMANOVA pseudo-F statistics. The

index and columns are sorted group names. - pvalues: pd.DataFrame containing pairwise PERMANOVA unadjusted p-values. The index and columns are sorted group names. - adjusted_pvalues: pd.DataFrame containing pairwise PERMANOVA adjusted p-values. p-values are adjusted for false discovery rate using Benjamini-Hochberg. The index and columns are sorted group names.