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# 18: Some Statistical Tools

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In this chapter we will look at some of the most basic and common approaches to applying statistical analysis to the attributes of actors embedded in networks, the relations among these actors, and the similarities between multiple relational networks connecting the same actors.

• 18.1: Introduction to Statistical Tools
Network analysis in the social sciences developed from a conjuncture of anthropologist's observations about relations in face-to-face groups and mathematical graph theory. A very large part of social network methodology, consequently, deals with relatively small networks, networks where we have confidence in the reliability of our observations about the relations among the actors. Most of the tools of social network analysis involve the use of mathematical functions to describe networks and thei
• 18.2: Describing One Network
Most social scientists have a reasonable working knowledge of basic univariate and bivariate descriptive and inferential statistics. Many of these tools find immediate application in working with social network data. There are, however, two quite important distinctive features of applying these tools to network data.
• 18.3: Comparing Two Relations for the Same Set of Actors
The basic question of bivariate descriptive statistics applied to variables is whether scores on one attribute align (co-vary, correlate) with scores on another attribute, when compared across cases. The basic question of bivariate analysis of network data is whether the pattern of ties for one relation among a set of actors aligns with the pattern of ties for another relation among the same actors. That is, do the relations correlate?
• 18.4: Explaining Attributes of Networked Actors
In the previous section we examined methods for testing differences and association among whole networks. That is, studying the macro-patterns of how an actor's position in one network might be associated with their position in another. We are often interested in micro questions, as well.
• 18.5: Explaining the Relations Among Actors in a Network
One of the most distinctive ways in which statistical analysis has been applied to social network data is to focus on predicting the relations of actors, rather than their attributes. Rather than building a statistical model to predict each actor's out-degree, we could, instead, predict whether there was a tie from each actor to each other actor. Rather than explaining the variance in individual persons, we could focus on explaining variation in the relations.
• 18.S: Some Statistical Tools (Summary)
In this chapter we've taken a look at some of the most basic and common approaches to applying statistical analysis to the attributes of actors embedded in networks, the relations among these actors, and the similarities between multiple relational networks connecting the same actors. We've covered a lot of ground. But, there is still a good bit more, as the application of statistical modeling to network data is one of the "leading edges" of the field of social (and other) network analyses.