Learning Statistics: Data, Methods, Inference

Definition and scope of statistics

Statistics is the discipline concerned with the collection, organization, analysis, interpretation, and presentation of data. In practice, it often begins with a statistical population (the full group of interest) or a statistical model, and then uses data collection plans such as survey design and experiment design. When a census is not possible, statisticians use sampling so that conclusions drawn from a sample can reasonably extend to the population. Statistics covers how data are gathered and studied through both experimental and observational approaches. Experimental studies involve manipulating a system and measuring outcomes to assess causal effects, while observational studies collect data without manipulation and examine associations. Two major branches of data analysis are descriptive statistics, which summarize data (e.g., mean and standard deviation), and inferential statistics, which use probability theory to draw conclusions about populations despite random variation such as sampling error and measurement error. A key part of inferential statistics is hypothesis testing and interval estimation, typically framed around a null hypothesis and an alternative hypothesis. Statistical tests quantify how evidence from data can lead to rejecting the null, while recognizing possible errors (Type I and Type II). Statistics also addresses measurement error, bias, missing data, and censoring, using specialized techniques to reduce or correct their impact.

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Statistical populations and statistical models

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