Statistics
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Statistics | |
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| Type | Scientific and mathematical discipline |
| Field | Mathematics; Data analysis |
| Core idea | Collection, analysis, interpretation, and communication of data under uncertainty |
| Assumptions | Data can inform inference; uncertainty can be quantified and managed |
| Status | Established field |
| Related | Probability theory; Statistical learning; Inference; Uncertainty |
Statistics is a discipline concerned with the collection, analysis, interpretation, and communication of data. It provides methods for drawing inferences from data in the presence of uncertainty and variability, and it is used across the natural sciences, social sciences, engineering, and public policy.
Statistics relies on formal models and assumptions to connect observed data to broader claims about populations, processes, or underlying structures.
Core idea
At its core, statistics addresses how conclusions can be drawn from data that are limited, noisy, or incomplete. Statistical methods aim to summarize patterns, quantify uncertainty, and support decisions based on evidence rather than anecdote.
Statistical reasoning does not eliminate uncertainty; it makes uncertainty explicit and manageable.
Descriptive statistics
Descriptive statistics focuses on summarizing and organizing data. Common tools include measures of central tendency, measures of variability, and graphical representations.
These methods describe what the data show without making claims beyond the observed sample.
Inferential statistics
Inferential statistics uses data from samples to make claims about larger populations or processes. This involves estimating parameters, testing hypotheses, and assessing the reliability of conclusions.
Inference depends on assumptions about how data were generated and how samples relate to the populations of interest.
Probability and models
Statistics is closely related to probability theory, which provides the mathematical framework for modeling uncertainty. Probabilistic models specify how data are expected to arise under different assumptions.
Statistical analysis evaluates how well models account for observed data and how sensitive conclusions are to modeling choices.
Estimation
Estimation concerns the use of data to infer unknown quantities, such as means, rates, or relationships between variables. Estimates are typically accompanied by measures of uncertainty that reflect sampling variability.
Different estimation methods trade off bias, variance, and robustness.
Hypothesis testing
Hypothesis testing provides formal procedures for assessing whether observed data are compatible with specific assumptions or claims. Test results depend on chosen significance criteria and underlying model assumptions.
The interpretation and use of hypothesis tests are subjects of ongoing debate within statistics.
Statistics and learning
Statistics provides foundational tools for statistical learning and machine learning. While learning systems emphasize predictive performance, statistical analysis emphasizes inference, uncertainty quantification, and theoretical guarantees.
The two perspectives address overlapping problems with different priorities.
Interpretation and limits
Statistical conclusions are conditional on assumptions about data quality, model structure, and relevance. Misinterpretation can arise when these assumptions are ignored or misunderstood.
Statistics clarifies what data can support and where conclusions exceed available evidence.
Status
Statistics is a mature and evolving discipline with broad applicability. Its primary role is to provide principled methods for reasoning from data while making uncertainty explicit and quantifiable.