Causal Inference in Introductory Statistics Courses

Figures & data

Fig. 1 A causal diagram depicting treatment A causing Y with no common causes.

Fig. 2 A causal diagram depicting treatment A, outcome Y, and confounding variable C.

Fig. 3 A causal diagram depicting treatment A, outcome Y, collider Z, and no causal effect of A on Y.

Fig. 4 A causal diagram depicting conditioning upon the confounder C.

Fig. 5 A causal diagram depicting treatment A, outcome Y, a confounder C we have adjusted for, and unmeasured confounders U. In this case, we cannot obtain valid estimates of the causal effect of A on Y.

Table 1 Description of variables in this study.

Variable	Description
AGE	Subject age (years)
FEV	Forced expiratory volume (L)
HEIGHT	Subject height (inches)
SEX	Biological sex: Female (0), Male (1)
SMOKE	Has the subject ever smoked? No (0), Yes (1)

Fig. 6 A causal diagram depicting relationships between variables in this study.

Table 2 Mean (standard deviation) by smoking status and sex.

	Female		Male
	SMOKE = 0	SMOKE = 1	SMOKE = 0	SMOKE = 1
n	279 (87.7%)	39 (12.3%)	310 (92.2%)	26 (7.8%)
AGE (years)	9.4 (2.7)	13.3 (2.2)	9.7 (2.8)	13.9 (2.5)
HEIGHT (inches)	59.6 (4.7)	64.6 (2.3)	61.5 (6.3)	68.1 (3.2)
FEV (liters)	2.4 (0.64)	3.0 (0.42)	2.7 (0.97)	3.7 (0.89)

Table 3 Estimates of the change in FEV (liters) comparing smokers to nonsmokers for two models.

Model	Estimate	95% C.I.
AGE and SEX adjusted (matching)	–0.08	(–0.22,0.08)
AGE and SEX adjusted (regression)	–0.15	(–0.31, 0.00)
Unadjusted	0.71	(0.49, 0.93)