Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data.
In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional, to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as “all persons living in a country” or “every atom composing a crystal”. Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.
“Statistical analysis,” “statistical methods,” “statistical techniques,” and “statistical tests” are related concepts in the field of statistics, but they serve different roles and have distinct purposes. Here are the key differences between these terms:
Statistical Analysis:
Definition: Statistical analysis is a comprehensive process that involves the collection, organization, cleaning, summarization, exploration, modeling, and interpretation of data using various statistical methods and techniques.
Purpose: The primary purpose of statistical analysis is to extract meaningful insights, patterns, and knowledge from data. It encompasses a wide range of tasks and statistical procedures, including data visualization, modeling, hypothesis testing, and making inferences.
Scope: Statistical analysis encompasses the entire workflow of working with data, from data preprocessing to the final interpretation of results. It is a holistic approach to understanding and drawing conclusions from data.
Statistical Methods:
Definition: Statistical methods refer to a broad set of tools, techniques, and approaches used in statistics for various purposes. These methods include data analysis, summarization, modeling, and inference, among others.
Purpose: Statistical methods serve a wide variety of purposes, such as data exploration, modeling relationships between variables, dimensionality reduction, clustering, and more. They can be applied at different stages of data analysis to achieve specific objectives.
Examples: Statistical methods include linear regression, logistic regression, principal component analysis (PCA), factor analysis, cluster analysis, survival analysis, and many others. These methods are used for different types of data and research questions.
Statistical Techniques:
Definition: Statistical techniques refer to specific procedures, algorithms, or tools that are used within the broader context of statistical analysis and methods. These techniques are employed to perform specific tasks, often with a focus on data manipulation, calculation, or modeling.
Purpose: Statistical techniques are applied to address particular questions or tasks during the data analysis process. They help achieve specific goals, such as summarizing data, testing hypotheses, or modeling relationships.
Examples: Statistical techniques include t-tests, chi-squared tests, ANOVA (Analysis of Variance), correlation analysis, factor rotation methods (e.g., Varimax), and clustering algorithms (e.g., k-means). These techniques are used to perform specific statistical tasks.
Statistical Tests:
Definition: Statistical tests are specific procedures or hypothesis-testing techniques used to make formal statistical inferences or decisions about a population based on a sample. They assess whether observed data provide enough evidence to support or reject a particular hypothesis.
Purpose: The primary purpose of statistical tests is hypothesis testing. These tests determine whether differences, relationships, or effects observed in sample data are statistically significant and not likely due to random chance.
Examples: Common statistical tests include t-tests (for comparing means), chi-squared tests (for testing associations in categorical data), hypothesis tests for population parameters (e.g., testing the population mean), and various non-parametric tests.
In summary:
Statistical analysis is the overarching process that includes all aspects of working with data, from data collection to final interpretation.
Statistical methods are the broad tools and techniques used for various data analysis tasks.
Statistical techniques are specific procedures or algorithms applied to perform particular statistical tasks.
Statistical tests are specific hypothesis-testing procedures used to make formal statistical inference