Statisticians use inferential statistics to reach conclusions that extend beyond the specific data studied, such as when using sample data to determine how a larger population might behave or respond to a specific stimulus. Inferential statistics can also compare the average performance between two groups, often through a device called the t-test.
The theoretical foundation of the majority of inferential statistics comes from the General Linear Model. This family of statistical models includes the t-test, regression analysis, and analysis of variance and covariance. Typically, when comparing groups through inferential statistics, statisticians use a dummy variable to represent the various groups being studied. Within the context of a statistical function or equation, one group may be designated by the discrete value 0 while the other one is designated by the value 1. This practice makes it possible to use a single equation to model two separate lines for two separate treatment groups and arrive at a conclusion about the relationship between them.
Typically, inferential statistics take place either within the structure of an experimental analysis or a quasi-experimental analysis. The primary difference between these two types of analysis is that in quasi-experimental analysis, researchers do not randomly assign units to groups. In this situation, statisticians often have to adjust their results before arriving at a statistically valid conclusion.