<P> Quantitative methods have limitations . These studies do not provide reasoning behind participants' responses, they often do not reach underrepresented populations, and they may span long periods in order to collect the data . </P> <P> Statistics is the most widely used branch of mathematics in quantitative research outside of the physical sciences, and also finds applications within the physical sciences, such as in statistical mechanics . Statistical methods are used extensively within fields such as economics, social sciences and biology . Quantitative research using statistical methods starts with the collection of data, based on the hypothesis or theory . Usually a big sample of data is collected--this would require verification, validation and recording before the analysis can take place . Software packages such as SPSS and R are typically used for this purpose . Causal relationships are studied by manipulating factors thought to influence the phenomena of interest while controlling other variables relevant to the experimental outcomes . In the field of health, for example, researchers might measure and study the relationship between dietary intake and measurable physiological effects such as weight loss, controlling for other key variables such as exercise . Quantitatively based opinion surveys are widely used in the media, with statistics such as the proportion of respondents in favor of a position commonly reported . In opinion surveys, respondents are asked a set of structured questions and their responses are tabulated . In the field of climate science, researchers compile and compare statistics such as temperature or atmospheric concentrations of carbon dioxide . </P> <P> Empirical relationships and associations are also frequently studied by using some form of general linear model, non-linear model, or by using factor analysis . A fundamental principle in quantitative research is that correlation does not imply causation, although some such as Clive Granger suggest that a series of correlations can imply a degree of causality . This principle follows from the fact that it is always possible a spurious relationship exists for variables between which covariance is found in some degree . Associations may be examined between any combination of continuous and categorical variables using methods of statistics . </P> <P> Views regarding the role of measurement in quantitative research are somewhat divergent . Measurement is often regarded as being only a means by which observations are expressed numerically in order to investigate causal relations or associations . However, it has been argued that measurement often plays a more important role in quantitative research . For example, Kuhn argued that within quantitative research, the results that are shown can prove to be strange . This is because accepting a theory based on results of quantitative data could prove to be a natural phenomenon . He argued that such abnormalities are interesting when done during the process of obtaining data, as seen below: </P>

Which of the following terms is part of quantitative research