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numpy-statistics

@cuba6112/skillfactory
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Standard and NaN-robust statistical functions for data analysis, histograms, and correlation matrices. Triggers: statistics, mean, nanmean, histogram, corrcoef, percentile, std.

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SKILL.md

name: numpy-statistics description: Standard and NaN-robust statistical functions for data analysis, histograms, and correlation matrices. Triggers: statistics, mean, nanmean, histogram, corrcoef, percentile, std.

Overview

NumPy provides a suite of statistical functions for summarizing data. Key capabilities include calculating central tendencies, dispersion, and relationships between variables, with specific handling for missing values (NaNs).

When to Use

  • Summarizing experimental data (mean, median, standard deviation).
  • Visualizing data distributions via histogram counts and binning.
  • Identifying relationships between multiple variables using correlation matrices.
  • Analyzing datasets with missing values where standard aggregations would fail.

Decision Tree

  1. Does your data contain NaN?
    • Yes: Use nan prefixed functions (e.g., np.nanmean).
    • No: Use standard functions (e.g., np.mean).
  2. Creating a histogram?
    • Need normalized area? Set density=True.
    • Fixed bin widths? Provide an integer for bins or an array for custom edges.
  3. Checking correlation?
    • Use np.corrcoef. Note: output may require clipping if float errors occur.

Workflows

  1. Robust Mean Calculation

    • Identify an array with potential missing values (NaNs).
    • Calculate the mean using np.nanmean(arr).
    • Optionally use np.nanstd(arr) to find the standard deviation of the valid subset.

  2. Custom Histogram Creation

    • Define a set of non-uniform bin edges [0, 5, 10, 50, 100].
    • Pass the data and edges to np.histogram(data, bins=edges).
    • Retrieve the counts and the validated edges for plotting.

  3. Inter-Variable Correlation Analysis

    • Stack multiple data variables into a 2D array (rows as variables).
    • Execute np.corrcoef(data).
    • Inspect the off-diagonal elements for Pearson correlation strengths.

Non-Obvious Insights

  • NaN Sensitivity: Standard statistical functions return NaN if even one element is missing; the nan versions are essential for real-world messy data.
  • Histogram Density: The density=True flag ensures the integral over the histogram is 1, not that the sum of the counts is 1 (unless bin widths are 1).
  • Precision Clipping: Correlation coefficients can occasionally drift outside [-1, 1] due to floating-point rounding; NumPy automatically mitigates this in corrcoef results.

Evidence

  • "nanmean... Compute the arithmetic mean along the specified axis, ignoring NaNs." Source
  • "Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability mass function." Source

Scripts

  • scripts/numpy-statistics_tool.py: Computes robust statistics and custom histograms.
  • scripts/numpy-statistics_tool.js: Basic mean calculator.

Dependencies

  • numpy (Python)

References