Sometimes researchers gain insights by manipulating raw data from a single database. For example, historians looking at 1860 census data can tell immediately the gross numbers of free persons, enslaved persons and slave owners living in the southern United States region at the time. But to gain an idea of the relative prevalence of slavery in the South, historians would need to look at the number of households claiming ownership of slaves and compare that to the total number of households. The proportion of slave-owning households would be an example of referential data derived from the other data.
Researchers often use measures of central tendencies as a way of analyzing raw data. The mean, mode, median and range all provide insight into how the raw data is grouped around certain points. Analysis of the central tendencies within a set of data enable researchers to make generalizations of the data, and of the population as a whole if the data is from a sample. More advanced measures, such as the normal distribution and standard deviation, allow researchers to make comparisons with other sets of data.
Inferential statistics is a more sophisticated method of looking at raw data. By looking at probability distributions and other derived data, researchers can formulate and test hypotheses about how different variables may interact with each other. For example, social scientists often look at data on socioeconomic status, and test how other variables, such as health or voting patterns, are related to it. They do this by finding the normal distribution of a set of data, and comparing that to a predicted normal distribution if there were no outside influences upon the data.
Meta-analysis is the combining of results of similar studies that address a related hypothesis. Researchers use meta-studies to see if results are more generalizable than those of individual studies, as well as to see if there is significant variation in results. Meta-studies are less prone to skewing from local influences than individual studies, and have higher statistical power. As long as the selection of the individual studies is not skewed, a meta-analysis can be a powerful tool for finding relationships that may not be statistically significant in smaller studies.