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| Instead, '''statistical inference''' is applied. In a random sample drawn from the population, observed statistics are estimators for the actual population parameters. When two random samples are drawn, one as an experimental group to which a treatment is applied and the other as a control group, any statistically significant difference is an estimator for actual causation. | Instead, '''statistical inference''' is applied. A tolerance for Type I error ''(false negatives)'' is determined, and from that a '''critical value''' is calculated. Experimental data is measured and, if the '''test statistic''' is greater than the critical value, the null hypothesis can be rejected. |
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| === Observation Study === | == Observational Study == |
Causal Inference
The fundamental goal of econometrics as a field is causal inference.
Contents
Causation
To study the impact of some treatment variable on an outcome variable, all other variables must be held constant. If a relationship can be observed ceteris paribus, then causation has been identified.
Experimental Design
A true causal experiment involves the application of a treatment. By comparing outcomes between an experimental group and an identical control group, causation can be observed and measured.
In Social Science
The unit of measurement in social science is almost always people. It isn't possible to source identical people for application of a treatment. As a result, true causal experiments are impossible in social sciences.
Instead, statistical inference is applied. A tolerance for Type I error (false negatives) is determined, and from that a critical value is calculated. Experimental data is measured and, if the test statistic is greater than the critical value, the null hypothesis can be rejected.
Given Ethics
There are non-negligible ethical barriers to conducting many experiments when the unit of measurement is people. This is mitigated only prohibitively, i.e. by use of Institutional Review Boards (IRBs). In other words, the body of causal experiments is limited by what is IRB approve-able.
Observational Study
Observational studies allow subjects to make decisions regarding the application of a 'treatment'. This absolves most ethical concerns, especially in social science.
But it is no longer necessarily true that the experimental and control groups are random and comparable. There are multiple non-redundant confounders which are related to the treatment and/or the outcome. These must be controlled for.