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Adding local short description: "Statistical technique to use observational data for causal analysis", overriding Wikidata description "statistical method" (Shortdesc helper) |
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: <math>y_{it} ~=~ \gamma_{s(i)} + \lambda_t + \delta I(\dots) + \varepsilon_{it}</math>
where <math>y_{it}</math> is the dependent variable for [[Sampling (statistics)|individual]] <math>i</math> and time <math>t</math>, <math>s(i)</math> is the group to which <math>i</math> belongs (i.e. the treatment or the control group), and <math> I(\dots) </math> is short-hand for the [[Dummy variable (statistics)|dummy variable]] equal to 1 when the event described in <math> (\dots) </math> is true, and 0 otherwise. In the plot of time versus <math>Y</math> by group, <math>\gamma_s</math> is the vertical intercept for the graph for <math>s</math>, and <math>\lambda_t</math> is the time trend shared by both groups according to the parallel trend assumption (see [[#Assumptions|Assumptions]] below). <math>\delta</math> is the treatment effect, and <math>\varepsilon_{it}</math> is the [[Errors and residuals in statistics|residual term]].
Consider the average of the dependent variable and dummy indicators by group and time:
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