Agenda

1. Recap: from Tutorial 1 to Tutorial 2
2. Statistical Models in R
   • Hypothesis testing — t-test & chi-square
   • Linear regression — lm()
   • Logistic regression — glm()

Agenda

3. Network Analysis in R
   • Why networks? Nodes & edges
   • Building & plotting graphs with igraph
   • Centrality — who is important?
   • Community detection
4. Hands-on

Where are we?

Tutorial 1 — the toolbox

• Variables, functions, data frames
• plot(), mean(), summary()

Tutorial 2 — putting the toolbox to work

• Ask questions of data → test & model → networks
• Two families of answers:
  • Statistical models: attributes of individuals
  • Network analysis: relations between individuals

Part I · Statistical Models

From description to inference

Descriptive statistics — what does my data look like?

• mean(), median(), summary(), plots (Tutorial 1)

Inferential statistics — is the pattern real? What explains it?

• Hypothesis testing: is this difference / association real?
• Modeling: how does x relate to y?

Both answer: "can I trust this pattern beyond my sample?"

Hypothesis testing (1)

A formal way to decide whether an observed pattern is "real"

• Null hypothesis (H0): nothing is going on (no difference, no association)
• Alternative hypothesis (H1): something is going on
• p-value: probability of seeing data like this if H0 is true
• Convention: p < 0.05 → reject H0 ("statistically significant")

p < 0.05 means "H0 looks unlikely", not "my theory is proven"

Hypothesis testing (2): t-test

Compare the means of two groups

t.test(mpg ~ am, data = mtcars)

• am = 0 (automatic) vs 1 (manual): is fuel efficiency different?
• Read the output: group means, t statistic, df, p-value

Digital sociology example: do verified accounts get more likes on average?

Hypothesis testing (3): chi-square test

Test the association between two categorical variables

tbl <- table(mtcars$cyl, mtcars$am)
chisq.test(tbl)

• H0: no association; p < 0.05 → associated
• Digital sociology example: is gender associated with platform choice?

Linear regression (1)

Model how a numeric outcome depends on predictors

• Fit the line that best describes y ~ x
• y = a + b·x + error
• lm(y ~ x, data = ...)

model <- lm(mpg ~ wt, data = mtcars)
summary(model)

(This is the line we drew in Tutorial 1's hands-on with abline())

Linear regression (2): reading the output

• Estimate (b): a one-unit increase in x → b change in y
• Pr(>|t|): is b significantly different from 0?
• R²: share of variation in y explained by the model (0–1)

Interpretation template:

"A 1,000 lbs heavier car is associated with 5.3 mpg lower fuel efficiency (p < .001)"

Linear regression (3): multiple predictors

model2 <- lm(mpg ~ wt + hp, data = mtcars)

• Now b means "holding the other variables constant"
• Categorical predictors → make them factors first (Tutorial 1!)

model3 <- lm(mpg ~ wt + factor(cyl), data = mtcars)

• Model comparison: does adding a variable help? (R², AIC)

Logistic regression (1)

When the outcome is binary (0/1, yes/no)

• Digital sociology: retweet or not? follow back or not? purchase or not?
• Why not lm()? → predicted values can go outside [0, 1]

model4 <- glm(am ~ wt + hp, data = mtcars, family = binomial)
summary(model4)

Logistic regression (2): interpretation

• Output is in log-odds — hard to interpret directly
• Convert to odds ratios:

exp(coef(model4))

• OR = 2 → the odds double per one-unit increase in x
• OR < 1 → negative association; OR > 1 → positive association

Which model when?

Rule of thumb: look at the outcome variable first

Part II · Network Analysis

Why networks?

Digital sociology studies relations, not only attributes

• Follows on Weibo/Twitter, retweets, replies, friendships
• Networks = individuals (nodes) + ties (edges)

Attribute view: who is this person? (age, gender, likes)
Network view: who is connected to whom? (position, influence, community)

Graph basics

• Nodes (vertices) — people, accounts, organizations
• Edges — ties between them
• Directed — A follows B ≠ B follows A
• Undirected — friendship: mutual
• Weighted — number of messages, strength of tie

Data format: edge list — a table with two columns: from, to

igraph: build & plot

library(igraph)

g <- graph_from_data_frame(edges, directed = TRUE)
plot(g)

• V(g) — nodes, E(g) — edges
• Add attributes: V(g)$name, V(g)$group

Classic example built into igraph: Zachary's karate club (1977)

make_graph("Zachary")

Network measures (1): degree & density

• Degree — how many ties a node has
  • in-degree: followers; out-degree: following
  • Digital sociology: the influencer = high in-degree

degree(g, mode = "in")

• Density — how connected the network is overall

edge_density(g)

Network measures (2): centrality

Who is "important" in the network?

• Degree centrality — most ties (popular, active)
• Betweenness centrality — on many shortest paths (bridges, gatekeepers)
• Closeness centrality — close to everyone else (information spreads fast)

betweenness(g)
closeness(g)

Different measures → different kinds of importance

Community detection

Find groups that are densely connected within, sparsely between

• The karate club: members split into two clubs — can the algorithm find it?

cm <- cluster_fast_greedy(g)
membership(cm)
plot(cm, g)

A social media example

• Edge list of user accounts: user_id follows followee_id
• Find the influencers (top in-degree)
• Visualize the community structure

igraph works the same way for 34 karate members and 34 million users

Hands-on

Part A · Statistical models (10 min)
Part B · Network analysis (10 min)

Hands-on A: Statistical models

Dataset: mtcars (continuation of Tutorial 1)

1. t-test — does fuel efficiency differ between automatic and manual cars?
2. Linear regression — model mpg with wt + hp; interpret coefficients and R²
3. Logistic regression — model am (automatic = 0, manual = 1); compute odds ratios

Hands-on B: Network analysis

1. Build the karate club network, plot it
2. Compute degree & betweenness — who are the top-3 most central?
3. Run community detection — compare with the real split
4. Load a small social media edge list (data/social_edges.csv) — find the top influencers and plot