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| title: Pearson Correlation Coefficient | |
| emoji: 🤗 | |
| colorFrom: blue | |
| colorTo: red | |
| sdk: gradio | |
| sdk_version: 3.19.1 | |
| app_file: app.py | |
| pinned: false | |
| tags: | |
| - evaluate | |
| - metric | |
| description: >- | |
| Pearson correlation coefficient and p-value for testing non-correlation. | |
| The Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases. | |
| The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. | |
| # Metric Card for Pearson Correlation Coefficient (pearsonr) | |
| ## Metric Description | |
| Pearson correlation coefficient and p-value for testing non-correlation. | |
| The Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases. | |
| The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. | |
| ## How to Use | |
| This metric takes a list of predictions and a list of references as input | |
| ```python | |
| >>> pearsonr_metric = evaluate.load("pearsonr") | |
| >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5]) | |
| >>> print(round(results['pearsonr']), 2) | |
| ['-0.74'] | |
| ``` | |
| ### Inputs | |
| - **predictions** (`list` of `int`): Predicted class labels, as returned by a model. | |
| - **references** (`list` of `int`): Ground truth labels. | |
| - **return_pvalue** (`boolean`): If `True`, returns the p-value, along with the correlation coefficient. If `False`, returns only the correlation coefficient. Defaults to `False`. | |
| ### Output Values | |
| - **pearsonr**(`float`): Pearson correlation coefficient. Minimum possible value is -1. Maximum possible value is 1. Values of 1 and -1 indicate exact linear positive and negative relationships, respectively. A value of 0 implies no correlation. | |
| - **p-value**(`float`): P-value, which roughly indicates the probability of an The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. Minimum possible value is 0. Maximum possible value is 1. Higher values indicate higher probabilities. | |
| Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases. | |
| Output Example(s): | |
| ```python | |
| {'pearsonr': -0.7} | |
| ``` | |
| ```python | |
| {'p-value': 0.15} | |
| ``` | |
| #### Values from Popular Papers | |
| ### Examples | |
| Example 1-A simple example using only predictions and references. | |
| ```python | |
| >>> pearsonr_metric = evaluate.load("pearsonr") | |
| >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5]) | |
| >>> print(round(results['pearsonr'], 2)) | |
| -0.74 | |
| ``` | |
| Example 2-The same as Example 1, but that also returns the `p-value`. | |
| ```python | |
| >>> pearsonr_metric = evaluate.load("pearsonr") | |
| >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5], return_pvalue=True) | |
| >>> print(sorted(list(results.keys()))) | |
| ['p-value', 'pearsonr'] | |
| >>> print(round(results['pearsonr'], 2)) | |
| -0.74 | |
| >>> print(round(results['p-value'], 2)) | |
| 0.15 | |
| ``` | |
| ## Limitations and Bias | |
| As stated above, the calculation of the p-value relies on the assumption that each data set is normally distributed. This is not always the case, so verifying the true distribution of datasets is recommended. | |
| ## Citation(s) | |
| ```bibtex | |
| @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 | |