Exercise 2 (20 minutes)

You practice: DAGs and a balance test — is racial appearance balanced across news readers? When you're done, assist some of the others …

(Keep working in the R script from Exercise 1 — you already have APAD prepared.)

1. Draw a DAG with a neighbour (pen and paper is fine). Start with two nodes — News consumption and Support for an anti-discrimination law — and an arrow from the first to the second. Now skim the APAD variables and add any confounders you can think of: a confounder needs an arrow into both nodes.

Some candidates

Age, German citizenship, immigrant generation, education, or racial appearance could all plausibly shape both how much news someone follows and their attitudes toward anti-discrimination law — each one opens a backdoor path.

2. Write it yourself: a balance test. The variable appearance records how a respondent's looks are typically described in Germany (White, Black, Asian, Arabic, Southern). Test whether appearance is balanced across news readers vs. non-readers.

Hint

select() just news_yn, appearance, and gewFAKT; rename(weights = gewFAKT) so it is treated as a weight; then datasummary_balance(~ news_yn, data = .).

R solution -> don't peek too early ;) !

APAD %>%
  select(news_yn, appearance, gewFAKT) %>%
  rename(weights = gewFAKT) %>%
  datasummary_balance(~ news_yn, data = .,
                      title = "Racial appearance of news readers vs. non-readers")

Racial appearance of news readers vs. non-readers

		0		1
		N	Pct.	N	Pct.
appearance	Arabic	14	6.4	58	6.6
	Asian	26	11.9	88	10.1
	Black	7	3.2	33	3.8
	Southern	58	26.6	263	30.1
	White	109	50.0	422	48.2

3. Read your balance table. What does it tell you? Appearance is perfectly balanced, so it cannot bias the comparisonThe groups differ in their racial-appearance mix — a sign the comparison is confoundedThe table proves that appearance causes news reading

4. Write one sentence (as a # comment) explaining why an imbalance in appearance matters for our estimate. Then compare:

Model answer

If people who are racialised differently both follow the news differently and face different levels of discrimination (and hold different views on anti-discrimination law), then appearance sits on a backdoor path — the raw news–attitude difference is partly selection bias, not a causal effect.

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5. Discuss with your neighbour — the limits of a balance test:

   1. A balance test can only check variables we measured. Name two unobserved confounders that are not in the APAD data but could bias the news effect.
   2. For each, say how it might shape news consumption and support for the law.
   3. Why can no balance test ever prove that a comparison is unbiased?

Talking points

(a/b) For example: political interest (drives more news and stronger pro-law attitudes); experiences of discrimination from family (shape both media diet and attitudes); trust in institutions; personality. (c) Balance on observed variables says nothing about the unobserved ones — and the baseline \(Y_0\) we truly care about is never seen. Only a design that makes the groups comparable by construction (next week: randomized experiments) can close every backdoor at once.