Scipy and Sklearn chi2 implementations give different results
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Chi-squared tests are a staple in statistics, often used to assess associations between categorical variables or to evaluate the goodness of fit. In Python, two prominent libraries, SciPy and Scikit-learn (sklearn), offer chi-squared test implementations. However, users might encounter divergent results between these two implementations due to differing use cases and methodological nuances. This article will delve into these differences, elucidate the reasons behind them, and provide relevant scenarios to showcase how they can impact analytics tasks.
SciPy vs. Sklearn: An Overview
SciPy
SciPy is a scientific library in Python, known for its mathematical, scientific, and engineering functionalities. Its chi-squared test is implemented in the `stats` module and is primarily oriented towards statistics. The test is invoked using `scipy.stats.chi2_contingency` or `scipy.stats.chisquare`, depending on whether a contingency table or a goodness-of-fit test is required.
Sklearn
Scikit-learn, on the other hand, is a machine learning library that provides various tools for data mining and data analysis. Its chi-squared test implementation is part of the `feature_selection` module, accessed via `sklearn.feature_selection.chi2`. This function is engineered to be used specifically for feature selection in pre-processing stages of machine learning pipelines, targeting the relevance of features with respect to a response variable.
Key Differences
| Aspect | SciPy | Sklearn |
| Primary Purpose | General statistical analysis | Feature selection for machine learning |
| Function | scipy.stats.chi2\_contingency, scipy.stats.chisquare | sklearn.feature\_selection.chi2 |
| Data Format | Contingency table (2D array) | Non-negative integer data arrays |
| Assumptions | May adhere closely to classic statistical test assumptions | Assumes feature independence by default |
| Result Interpretation | p-value for hypothesis testing | Chi-square statistic useful for feature scores |
| Correction for Continuity | Yates' correction (if applicable) | None |
Technical Explanation
Different Purposes and Data Requirements
SciPy's Chi-Squared Test
SciPy's implementations are closer to textbook definitions of chi-squared tests. They require input in the form of a contingency table for chi-square independence tests, or a count of observed vs. expected frequencies for goodness-of-fit tests. The interpretations are based on traditional statistical frameworks—yielding a test statistic and a p-value to infer statistical significance.
Example with SciPy:
- SciPy optionally employs Yates' correction for continuity in a 2x2 table, which adjusts the chi-square statistic for better approximations with smaller sample sizes.
- Sklearn's implementation does not apply such corrections, focusing purely on the feature's utility as measured by the chi-square statistic.
- SciPy's chi-squared test can handle broader types of input arrays, including expected probabilities or observed frequencies beyond count data.
- Sklearn mandates non-negative integer data since it's designed with feature selection for classification tasks in mind.
- SciPy provides both a chi-squared statistic and a p-value to ascertain statistical significance explicitly.
- In Sklearn, while a chi-squared statistic is provided, the focus is more on the feature's scoring potential rather than a standalone inferential statistic.
- Data Preprocessing: Ensure datasets fed into Scipy's functions are properly formatted in contingency tables if performing an independence test, whereas Sklearn requires features and labels to be pre-arranged for proper computation.
- Understanding Results: Be clear on the test objectives - for inferential statistics, use SciPy. For feature-ranking in classification problems, Sklearn is more beneficial.
- With imbalanced classes or small sample sizes, results from both implementations could be misleading. Delving deeper into diagnostics or combining chi-squared results with other methods (like cross-validation in ML contexts) can offer more robust insights.
