Defined as psychological research which performs mathematical modeling and statistical estimation or statistical inference. This definition distinguishes it from so-called qualitative psychological research; however, many psychologists do not acknowledge any real difference between quantitative and qualitative research. The validity of the distinction is discussed in the article about qualitative psychological research.
Statistics is widely used in quantitative psycological research. Typically a project begins with the collection of data based on a theory or hypothesis, followed by the application of descriptive or inferential statistical methods. Often it is necessary to collect a very large volume of data, which require validating, verifying and recoding. Software packages such as PSPP and R are typically used for this purpose, and for subsequent analysis. Causal relationships are studied by manipulating factors thought to influence the phenomena of interest while controlling other variables relevant to the experimental outcomes. Researchers might measure and study the relationship between education and measurable psychological effects, whilst controlling for other key variables. Quantitatively based surveys are widely used by psychologists, and statistics such as the proportion of respondents who display one or more psychological traits reported. In such surveys, respondents are asked a set of structured questions and their responses are tabulated. The software can then perform correlation analysis or other procedures on the data.