Statistical Analysis

Statistical analysis techniques analyze and interpret data to draw meaningful conclusions, identify patterns, make predictions, and test hypotheses. This skill maps the technique family; several more specific methods elsewhere in this collection (Bayes Theorem Analysis, Chi Square Analysis, Monte Carlo Analysis) are each one specific tool within it.

The technique family

• Descriptive statistics — summarize a dataset's main characteristics: mean, variance, standard deviation. Describes what the data is, without generalizing beyond it.
• Inferential statistics — generalizes from a sample to a larger population: confidence intervals, t-tests, analysis of variance, regression analysis, chi-square tests (see Chi Square Analysis for that one specifically).
• Regression analysis — examines the relationship between a dependent variable and one or more independent variables: linear, multiple, logistic, and polynomial regression, each suited to different data shapes and relationship types.
• Time series analysis — studies patterns, trends, and seasonality in data over time: moving averages, exponential smoothing, ARIMA models (see Trend Analysis for the applied version of this).
• Factor analysis — identifies underlying, unobserved factors explaining correlations among observed variables.
• Cluster analysis — groups observations by similarity: k-means, hierarchical clustering, DBSCAN — related to but distinct from Anomaly Analysis's use of clustering specifically to flag points that don't fit any cluster well.
• Data mining — discovering patterns, relationships, and insights in large, complex datasets: decision trees (see Decision Tree), random forests, support vector machines, neural networks.

Choosing among them

The right technique follows from the actual question: describing what already happened (descriptive), generalizing from a sample (inferential), quantifying a relationship between variables (regression), understanding change over time (time series), finding hidden structure (factor/cluster analysis), or discovering unexpected patterns in a large dataset (data mining). A common mistake is reaching for a familiar technique regardless of fit — e.g. running a regression when the actual question is really about categorical association, which calls for Chi Square Analysis instead.

Common pitfalls

• Applying inferential statistics to a non-representative sample — generalizing from a biased or unrepresentative sample to the broader population produces confident-sounding but invalid conclusions.
• Confusing correlation (from a regression or cluster finding) with causation — a strong statistical relationship doesn't by itself establish which variable, if either, causes the other.
• Picking a technique for familiarity rather than fit — see above; the right tool follows from the actual data type and question, not from whichever method the analyst already knows best.
• Ignoring a technique's underlying assumptions — most of these methods have real prerequisites (data distribution shape, sample independence, minimum sample size); violating them, as Chi Square Analysis notes for its own small-expected- frequency caveat, can silently invalidate the result.

Learn more

• Bayes Theorem Analysis, Chi Square Analysis, Monte Carlo Analysis for specific techniques within this family, covered in depth.
• Trend Analysis, Anomaly Analysis for applied time-series and outlier-detection techniques.
• Decision Tree for the data-mining technique also used as a general business decision-evaluation tool.