Key Concepts in Network Analysis and Correlation Statistics

geodesic distance

The length of the shortest path between two nodes in a network. Example: W9 to S1 = 2; S4 to W1 = 4.

centrality

A node's position in a network based on structure, not personal traits.

centralization in a network

A group-level measure showing how much ties revolve around a central node. Star network = high centralization.

density

It's the number of actual ties divided by the number of possible ties. Undirected: T / [n(n-1)/2]; Directed: T / n(n-1).

clustering coefficient

A measure of how tightly nodes are clustered together in a network.

triad census

A count of all 3-node patterns in a network.

eigenvector centrality

A centrality score that increases if you're connected to other well-connected nodes. Think: popular friends boost your score.

eigenvector centrality in disconnected networks

It only gives values to the largest connected component.

Beta centrality

What should you use instead of eigenvector centrality for directed networks?

closeness centrality

It's the total distance from a node to all others. Lower = more central.

betweenness centrality

Measures how often a node sits on the shortest paths between others. High = strong position to broker or control flow.

bridging player in network analysis

A person who connects otherwise separate clusters or groups.

component in a network

A set of nodes that are all connected, directly or indirectly.

strong component

A component that respects the direction of ties.

weak component

A component that ignores direction and treats ties as undirected.

finding components in NetDraw

Go to Analysis → Components.

correlation in statistics

A measure of how two variables move together. Positive = increase together; Negative = one increases while the other decreases.

Pearson correlation

Measures strength of a linear relationship between two continuous variables. Requires normality and is sensitive to outliers.

Spearman correlation

A non-parametric measure for monotonic relationships. Good with ordinal data and not affected by outliers.

difference between simple and multiple correlation

Simple = 2 variables. Multiple = 3 or more variables studied at once.

positive correlation example

More study time → higher grades.

negative correlation example

More TV time → lower grades.

How do you add a linear fit line to a scatterplot in SPSS?

Double-click graph → Chart editor → Elements → Fit line at total → Select Linear → Apply.

How do you interpret a Pearson correlation of 0.428 with a p-value < 0.001?

There is a moderate, statistically significant positive relationship.

What does a p-value less than 0.05 mean?

The result is statistically significant and not likely due to chance.

What does a p-value greater than 0.05 mean?

The result is not statistically significant—we fail to reject the null hypothesis.

What is the "black swan" analogy for p-values?

Seeing one black swan disproves the idea that all swans are white. A low p-value = surprising result → reject the original claim.

What is the null hypothesis (H0)?

A statement that there is no relationship between two variables.

What is the alternative hypothesis (H1)?

A statement that there is a relationship between the variables.

What is an unstandardized regression coefficient (B)?

It shows how much the dependent variable is expected to change for a one-unit change in the predictor.

How do you interpret B in a regression equation?

If B = 0.057, then each additional year of age predicts a $0.057 increase in compensation.

What is a standardized regression coefficient (Beta)?

A unit-free measure showing how many standard deviations the outcome changes per standard deviation change in the predictor.

Why use standardized coefficients?

To compare the effect sizes of different variables measured in different units.

What is the regression equation using B0 and B1?

Y = B0 + B1X + ε. Example: Compensation = -2.19 + 0.057 * Age.

What does a scatterplot with a linear fit line show?

It visually shows the relationship between two variables. A positive slope = positive relationship.

What is dyadic-level analysis in networks?

Analysis that focuses on pairs of nodes and their relationships.

What is node-level analysis?

Focuses on individual nodes and their attributes or positions in the network.

What is group- or network-level analysis?

Focuses on the overall network structure, like density and centralization.

What is a QAP correlation?

A statistical test that uses permutations to measure the correlation between dyadic matrices.

What is MRQAP?

A regression model for dyadic data using multiple predictors and permutation testing.

How does QAP work?

It calculates a real correlation, then shuffles data many times (e.g., 20,000) to see how likely that correlation is by chance.

What does the p-value from a QAP test mean?

It shows the likelihood that the observed correlation is due to random chance. If < 0.05, it's significant.