3.2.2. Statistical Methods for Data Understanding

First Principle: Applying statistical methods fundamentally provides a quantitative understanding of data distributions, central tendencies, variability, and relationships, forming the basis for informed feature engineering and model building.

Beyond visualizations, statistical methods provide a quantitative foundation for understanding the characteristics of your data. This is crucial for making informed decisions during feature engineering and model selection.

Key Statistical Methods for Data Understanding:

• Measures of Central Tendency:
  • Mean: Average value. Sensitive to outliers.
  • Median: Middle value. Robust to outliers.
  • Mode: Most frequent value. Useful for categorical data.
• Measures of Dispersion (Variability):
  • Range: Difference between max and min.
  • Variance: Average of the squared differences from the mean.
  • Standard Deviation: Square root of variance. Measures spread around the mean.
  • Interquartile Range (IQR): Range between the 25th and 75th percentiles. Robust to outliers.
• Measures of Shape:
  • Skewness: Measures the asymmetry of the probability distribution of a real-valued random variable about its mean.
  • Kurtosis: Measures the "tailedness" of the probability distribution of a real-valued random variable.
• Frequency Distributions: For categorical data, counts of each category.
• Percentiles/Quantiles: Describe the position of a value relative to others in a dataset.
• Hypothesis Testing:
  • T-tests, ANOVA: Comparing means of groups.
  • Chi-squared test: Testing for independence between categorical variables.
• Correlation: (See 3.2.3) Measures the linear relationship between two numerical variables.

Importance for ML:

• Understanding Data Distributions: Helps determine if features need transformation (e.g., skewed data might need log transformation).
• Outlier Detection: Statistical measures like Z-score and IQR are common for identifying outliers.
• Feature Importance: Statistical tests can help understand the relationship between features and the target variable.
• Missing Value Imputation: Inform choices for imputation methods (e.g., using median for skewed data).

AWS Tools:

• SageMaker Notebook Instances / Studio Notebooks: Use Python libraries like Pandas (.describe(), .value_counts()), NumPy, and SciPy for detailed statistical analysis.
• Amazon Athena: Perform aggregate SQL queries (AVG, MEDIAN, STDDEV, COUNT, MIN, MAX) directly on large datasets in S3.
• SageMaker Data Wrangler: Generates data quality reports with descriptive statistics and data distribution insights.

Scenario: You are analyzing a dataset of customer incomes and spending habits. You need to understand the typical income range, how spread out the incomes are, and if the distribution is skewed. You also want to verify if a categorical feature (e.g., "customer_segment") is statistically independent of another categorical feature (e.g., "preferred_product_type").

Reflection Question: How does applying statistical methods (e.g., calculating mean/median/standard deviation, using Chi-squared test for independence) fundamentally provide a quantitative understanding of data distributions, central tendencies, variability, and relationships, forming the basis for informed feature engineering and model building?