A statistical model describes relationships between variables. Does one thing change another? Does one thing relate to another? Is something different from another in a fixed way? Can a large population be expected to follow along the same lines as a sample?
The first important charasteric of a model is a statement about the precision with which the statistics of effect describe the model, which describes the populaton. Confidence limits and P-values provide that statement.
There are several types of models, beginning with the basic straight line model of two variables. The observations are posed in relation to a straight line: if less of one variable is expected to relate to less of another variable then the line will slant upward from left to right. A calculation called the correlation coefficient will tell if the observations fit into that expectation and how well they fit. The P-value, or confidence calculation will tell if there is even a line at all!
There are models for numeric variables, where numbers represent the information. Nominal variables are represented by levels or have names. Some models test the relationships between numeric variables, nominal variables, or a combination of the two types of variables.
Some of the classic statistical models include the linear regression model, which looks for less of variable A to relate to less of variable B, or a line that goes from lower left to upper right.
The T-Test, also known as the Student’s T, or simply “T” tests whether a numeric variable relates to a nominal variable. A Paired T-Test allows several variables to be compared.
The Contingency table tests the ways in which two nominal variables relate to each other. A table is made where the numbers of observations that fall into categories, such as women who like shoes, women who hate shoes, men who like shoes, men who hate shoes. The Chi squared test determines if there is a relationship between sex and love (or hate) of shoes, for example.
Categorical modeling allows nominal variables to be related to numeric variables. A person’s preference in music versus age, for example is a complicated matter, where a categorical model can be used to determine if there is a relationship and how strong it is.
There are many more details and complexities to statistical modeling, just as there are more statistical models. A most excellent resource for gaining a basic understanding is provided in the Citation.
Will G. Hopkins, “A New View of Statistics”, 2001