metadata

title: Spearman Correlation Coefficient Metric
emoji: 🤗
colorFrom: blue
colorTo: red
sdk: gradio
sdk_version: 3.19.1
app_file: app.py
pinned: false
tags:
  - evaluate
  - metric
description: >-
  The Spearman rank-order correlation coefficient is a measure of the
  relationship between two datasets. Like other correlation coefficients, this
  one varies between -1 and +1 with 0 implying no correlation. Positive
  correlations imply that as data in dataset x increases, so does data in
  dataset y. Negative correlations imply that as x increases, y decreases.
  Correlations of -1 or +1 imply an exact monotonic relationship.

  Unlike the Pearson correlation, the Spearman correlation does not assume that
  both datasets are normally distributed.

  The p-value roughly indicates the probability of an uncorrelated system
  producing datasets that have a Spearman correlation at least as extreme as the
  one computed from these datasets. The p-values are not entirely reliable but
  are probably reasonable for datasets larger than 500 or so.

Metric Card for Spearman Correlation Coefficient Metric (spearmanr)

Metric Description

The Spearman rank-order correlation coefficient is a measure of the relationship between two datasets. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Positive correlations imply that as data in dataset x increases, so does data in dataset y. Negative correlations imply that as x increases, y decreases. Correlations of -1 or +1 imply an exact monotonic relationship.

Unlike the Pearson correlation, the Spearman correlation does not assume that both datasets are normally distributed.

The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Spearman correlation at least as extreme as the one computed from these datasets. The p-values are not entirely reliable but are probably reasonable for datasets larger than 500 or so.

How to Use

At minimum, this metric only requires a list of predictions and a list of references:

>>> spearmanr_metric = evaluate.load("spearmanr")
>>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4])
>>> print(results)
{'spearmanr': -0.7}

Inputs

predictions (list of float): Predicted labels, as returned by a model.
references (list of float): Ground truth labels.
return_pvalue (bool): If True, returns the p-value. If False, returns only the spearmanr score. Defaults to False.

Output Values

spearmanr (float): Spearman correlation coefficient.
p-value (float): p-value. Note: is only returned if return_pvalue=True is input.

If return_pvalue=False, the output is a dict with one value, as below:

{'spearmanr': -0.7}

Otherwise, if return_pvalue=True, the output is a dict containing a the spearmanr value as well as the corresponding pvalue:

{'spearmanr': -0.7, 'spearmanr_pvalue': 0.1881204043741873}

Spearman rank-order correlations can take on any value from -1 to 1, inclusive.

The p-values can take on any value from 0 to 1, inclusive.

Values from Popular Papers

Examples

A basic example:

>>> spearmanr_metric = evaluate.load("spearmanr")
>>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4])
>>> print(results)
{'spearmanr': -0.7}

The same example, but that also returns the pvalue:

>>> spearmanr_metric = evaluate.load("spearmanr")
>>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4], return_pvalue=True)
>>> print(results)
{'spearmanr': -0.7, 'spearmanr_pvalue': 0.1881204043741873
>>> print(results['spearmanr'])
-0.7
>>> print(results['spearmanr_pvalue'])
0.1881204043741873

Limitations and Bias

Citation

@book{kokoska2000crc,
  title={CRC standard probability and statistics tables and formulae},
  author={Kokoska, Stephen and Zwillinger, Daniel},
  year={2000},
  publisher={Crc Press}
}
@article{2020SciPy-NMeth,
  author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and
            Haberland, Matt and Reddy, Tyler and Cournapeau, David and
            Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and
            Bright, Jonathan and {van der Walt}, St{\'e}fan J. and
            Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and
            Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and
            Kern, Robert and Larson, Eric and Carey, C J and
            Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and
            {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and
            Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and
            Harris, Charles R. and Archibald, Anne M. and
            Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and
            {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},
  title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific
            Computing in Python}},
  journal = {Nature Methods},
  year    = {2020},
  volume  = {17},
  pages   = {261--272},
  adsurl  = {https://rdcu.be/b08Wh},
  doi     = {10.1038/s41592-019-0686-2},
}

Further References

Add any useful further references.