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I took your 29 values and used my tool of choice , which I have helped to develop. In order to assess the statistical importance of your candidate predictor variable X , one needs to address the question of unusual activity in either the X or the Y variable. The hypothesis that a possibly change in X at period 21 is dealt with by introducing a candidate ...


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It seems to me that your question is more contextual than mathematical. If I understand your data correctly, you are measuring the number of visitors, we'll call this $V$ and measuring some second variable we'll call $X$. I'm not sure where you're running a t-test here, because a t-test requires a categorical variable, which I do not see in your data. ...


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There are a few problems with what you've written, some of which are minor. First, the true ATE is $$E[y(1)] - E[y(0)]$$where $y_i(a)$ is the potential outcome under treatment level $a$. Without assumptions, this quantity cannot be estimated because $y_i(1)$ and $y_i(0)$ are not observed for any units. Randomization gives us the assumption of ...


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Non-Response For non-response, you would use something more like inverse probability of sampling weights. THIS PAPER describes the inverse probability weights you might consider and the overall process. While it is described in the context of a randomized trial and a general population, there is a clear parallel to the scenario you describe. As for ...


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An exchange of comments with @Alexis (and their correspondence with Pearl himself) cleared things up for me. I can summarize as follows: For the exogenous variables $U_X, U_Y, U_Z$ we only allow/count double arrows (just... because?). For these variables we have three missing (double) arrows, which are $U_X \leftrightarrow U_Y, U_Z \leftrightarrow U_Y$ and $...


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If you assume zero covariance between $\epsilon^1_t$ and $\epsilon^2_t$ as well as between $y_{t-1}$ and $\epsilon^2_t$, then $\beta$ is identified by a regression of $y_t$ on $x_t$ and $y_{t-1}$. This then identifies $cov(x_t, \epsilon^1_t) = cov(x_t, y_t - \beta x_t) = cov(x_t, y_t) - \beta var(x_t)$. If you assume zero covariance between $\epsilon^1_t$ ...


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For binary data correlation does not suit well, but there are many similarity indexes that you can use like the Jaccard index (https://en.wikipedia.org/wiki/Jaccard_index).


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I'm going to focus on a narrow topic: what if you can't do a two group experiment, either randomized or observational? What if you have only one group? Or what if you are talking about some national policy change where, because the change happened to the entire country, there's no obvious control group? I think you can attribute causation in some limited ...


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You can not find causation with analysis of the same data which shows correlation. Sammy above gave an example of hypothesis: living in big cities causes mental disorders. The study he proposes have only two features: location and mental disorder status, and it can show only correlation, not causation. There is always a possibility that people with ...


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Not sure this adds anything, but if you need another thought from philosophy, back in the day, (1960s) we were taught in a philosophy class that Hume’s 3 criteria of causality required: (1) temporal precedence (presumed cause prior in time); (2) an observable empirical correlation; and (3) that all rival hypotheses had been ruled out. Assuming criteria #3 ...


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Briefly... Option 1: Randomized Controlled Trial. The 'gold standard'. Option 2: Draw a causal diagram of your system. A directed acyclic graph of how you and others think the system operates. Decide if one can infer causation from observational study, by the back door criterion, front door criterion, or other conditional independence methods. Collect ...


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