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Earlier today I was discussing statistical analysis software with a colleague of mine. My colleague had primarily used SPSS in previous work for performing t-tests, anovas, manovas, and other statistical tests similar to those. My colleague also mentioned that SPSS does not handle regressions well. I have no idea whether or not SPSS handles regressions well, but I did respond that a t-test can be formulated as a regression, so SPSS must not be all that bad with regressions. We got to talking about t-tests, regression, and causality, and it came up that "you cannot prove causality with regression, while t-tests are able to prove causality." I've always thought that causality could be established given an appropriate experimental design, regardless of whether you use a t-test or regression to estimate something or perform a hypothesis test. Is it possible to establish a causal relationship using a t-test and not regression? Is it possible to establish a causal relationship without knowing about the experimental design?

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SPSS, compared to R, Stata, and SAS, is really relatively worse in handling regression (at least in its REGRESSION command), because it does not create binary indicator for you (dummy variables) if you have a categorical predictor. While other software packages can deal with it easily with one extra option/command line. To circumvent that problem, SPSS users often have to use GLM, which is fine, but difficult for learners. –  Penguin_Knight Oct 23 '12 at 18:04
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Perhaps I am being picky, but statistical tests do not prove causality, one way or another, but they can show strong evidence if conducted properly. Second, social scientists often show causality through regressions, for example in an IV regression. –  kirk Oct 23 '12 at 20:24
    
@Penguin_Knight That's an interesting flaw (? maybe it's intentional) of SPSS. –  Max Oct 24 '12 at 0:02
    
@kirk You're not being picky. That's a fair point, and one that I will keep in mind when I encounter causality in the future. What's more interesting is that the person I was conversing with was trained in psychology. –  Max Oct 24 '12 at 0:04
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@John is correct, but, in addition you cannot prove causation with any experimental design: You can only have weaker or stronger evidence of causality.

In any study, but especially in an observational study, evidence for causality is increased by including relevant covariates, giving a scientifically plausible causal path, replicating results and so on.

However, even in the best experimental design, you don't prove causality.

As for t-tests vs. regression - your friend does not know what he/she is talking about. T-tests results can be duplicated exactly with regression procedures: Just use a single independent variable that is dichotomous.

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Causal relationships are established by experimental design, not a particular statistical test. You could use a correlation as your statistical test and demonstrate that the true experiment you conducted showed causation. You could perform a t-test as your statistic and show a relationship in your quasi or observational study that does not motivate a causal explanation.

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