## 1.7 Descriptive inference, causal inference & prediction

• Q: What is the difference?
• Q: What does the “inference” in statistical inference stand for?

### 1.7.1 Descriptive questions

• How are observations distributed across values of Y? (univariate)2
• e.g. How are individuals (observations) distributed across values of trust?

Table 1.1: Univariate distribution of trust (2006)
0 1 2 3 4 5 6 7 8 9 10
303 42 172 270 369 1281 853 1344 1295 353 356

• How are observations distributed across values of Y and X?
• How are observations distributed across trust and gender values?
• We can add as many variables/dimensions as we like
• How are observations distributed across trust, gender and time values?
• Normally we summarize those distributions using models
• e.g. means of trust across gender across time
• Sometimes this is called associational inference (Holland!)!

### 1.7.2 Causal questions

• Is there a causal link between the distribution across values of Y and values of D?
• Do differences in D cause differences in Y? (see app)
• Would individual i have another level trust (Y), had it not been victimized (D)? (Bauer 2015)
• …in practice we tend to summarise those distributions..
• Continuous variables: Compare means
• Categorical variables (several): Compare probabilites for categories

Table 1.2: Joint distribution of trust and victimization (2006, N = 6633)
0 1 2 3 4 5 6 7 8 9 10
no victim (0) 259 36 135 214 320 1142 782 1228 1193 326 331
victim (1) 44 6 37 56 48 139 70 114 101 27 25

• Q: How do we calculate the mean?
• The mean of trust for non-victims is 6.2, the mean of trust for victims is 5.48.

### 1.7.3 Prediction

• Q: What does prediction look like?
• Quick summery…and more on that later!

### References

Bauer, Paul C. 2015. “Negative Experiences and Trust: A Causal Analysis of the Effects of Victimization on Generalized Trust.” Eur. Sociol. Rev. 31 (4): 397–417.

Gerring, John. 2012. “Mere Description.” British Journal of Political Science 4 (4): 721–46.

1. See Gerring (2012) for a discussion of “What?” and “Why?” questions.