Jan, I think your "type II concept" is not an alternative concept of causality. Causality remains the deterministic relation beween event "A" and a aubsequent event "B". However, neither "A" nor "B" might be deterinable with enough precision, and many other events may play a (deterministic) role. Therefore we are just unable to directly see this strict A->B relation, and we can only be happy to find some more or less tight statistical correlation between A and B.

Antonio, the concept of cause and effect is a mental model. It can be useful under some circumstances and not under other circumstances.The first question is: "Is a causal model (mentally!) relating two variables beneficial in some way?" and the second question is then: "Is there any logical reason (from other causal models) obviating the integration of this causative model into the meta-model?", and, finally, the question: "Does the available data contradict the cause-effect model?"

Data *alone* can never tell us something about a "reality" and not even about the usefulness of a model. We have to have a concept in mind, and then we can judge how and how much observed data should change our point of view. Thus, a correlation might be (more or less) convincing to assume a cause-effect relationship, when it is in-line with the meta-model (with the whole rest of our "understanding" of the world). Otherwise we would just recognice the correlation and probably think of different model including a common cause for both variables (example: correlation between the number of storks and babies; a reasonable common "cause" is the industrialisation).

In many cases the integration of the time in the analysis might help. An effect must come after the cause. Observing the opposite would make a cause-effect model unreasonable.

Reasonability - this is the key word here. It does not come from data alone, only in conjunction with a mental concept (based on much more knowledge and convictions), and with aims we have. Therefore, no data will ever "suggest" a cause-effect relationship by itself. But it can be (not) well in-line with a mental model of such a relationship, and such a model may (not) be useful for some purpose.

Statistical methods only provide means to measure how "tight" a relationship is, but only -again!- for an already assumed functional form of this relationship (and for the already assumed importance of the considered variables, co-variables, confounders...).

In the area of statistics there is an area called Experimental Design, which is specifically looking for evidence on the effect Set (type and quantity) that could cause one or more variables.

But that is the appropriate variables are not the subject of statistics, but who generates the investigative process.

Is, for example. generates critical thinking better reading comprehension, reading comprehension or critical thinking developer, this should be built based on the theory that supports the hypothesis raised. The statistics will be tasked to show what you build. Us! Have some signs, but the expert must deciphering to find the truth.

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a good read :

Probability, Causality and the Empirical World: A Bayes–de Finetti–Popper– Borel Synthesis

A. P. Dawid

Statist. Sci. Volume 19, Number 1 (2004), 44-57.

Abstract

This article expounds a philosophical approach to Probability and Causality: a synthesis of the personalist Bayesian views of de Finetti and Popper’s falsificationist programme. A falsification method for probabilistic or causal theories, based on “Borel criteria,” is described. It is argued that this minimalist approach, free of any distracting metaphysical inputs, provides the essential support required for the conduct and advance of Science.

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdfview_1&handle=euclid.ss/1089808272

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and another (different) one :

J. Pearl, "Causal inference in statistics: An overview," Statistics Surveys, 3:96--146, 2009

Abstract: This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret,” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.

http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf

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regarding the call, the "non-invertibility" criterion seems somewhat puzzling to an (ex-) physicist ... the remanent magnetization of a ferromagnet is typically a non invertible function of the external magnetic field ("hysteresis" phenomenon ; http://en.wikipedia.org/wiki/Hysteresis ) : most physicists would however agree on the fact the remanent magnetization is a consequence of the external magnetic field. (And they would certainly add that it also depends on the past values of this external field.)

moreover, in the evaluation of the results, mixing the "A and B are independent" and "A and B are consequences of a common cause" as a single "null" class "between" "a causes B" and "B causes A" is quite arguable.

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Granger causality is your answer. However, when you write up your results you cannot say "A causes B". You say "A Grander causes B" and vice versa.

The solutions of the other writers would not be stated by Statisticians and Data Analysts. I am sure they are expert in their fields but there answers to you are not good.

I believe no "statistical way" can prove a causal relationship. To prove X is the cause of Y, some premises are needed. As Simon (1954) suggested, three conditions, including precede(X happens before Y)、correlation (between X, Y) and spurious(no any third variable can explain relationship between XY) are needed to guarantee the causal relationship. From this perspective, “precede” could not be attained by only statistics, and “spurious” is almost impossible unless you collect “all” possible third variables as covariates. Therefore, no "statistical way" can prove a causal relationship. Some people (Crano & Brewer, 2002) believed that experimental design is the only way can proved causal relationship (I strongly agree with this view point).

Please read again!! Granger Causality is not "causality." However, under the assumptions of Granger methodology you may use the phrase "Granger Cause."

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Jan, i share your view on Pearl's monumental work (maybe i am more sensitive to the efforts deployed to provide a rigorous framework and debunk simplistic statements about what causality might mean in a standard statistical framework) ; you'll even find a link between an extension of Pearl's Causal Model ("Settable Systems") and Granger's Causality in

Linking Granger Causality and the Pearl Causal Model with Settable Systems

H. White et al

JMRL: Workshop and Conference Proceedings 12 (2011) 1-29

Workshop Causality in Time Series

The causal notions embodied in the concept of Granger causality have been argued to belong to a different category than those of Judea Pearl’s Causal Model, and so far their relation has remained obscure. Here, we demonstrate that these concepts are in fact closely linked by showing how each relates to straightforward notions of direct causality embodied in settable systems, an extension and refinement of the Pearl Causal Model designed to accommodate optimization, equilibrium, and learning. We then provide straightforward practical methods to test for direct causality using tests for Granger causality.

http://fmwww.bc.edu/EC-P/wp744.pdf‎

as i have always been reluctant to admit that the causality link between two observations might depend upon the representations we choose for the observations (such as the intriguing "X G-causes Y" but "LogX does not G-cause LogY" --oh i know, i should write "we cannot reject the fact that "LogX does not GC cause LogY"", even if i'm not a true native of Statistikstan nor of the United States of Datana ;) ), i appreciate the ultra-minimalist approach advocated by Dawid.

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I thank you all for offering so many interesting points for reflection. Naturally, I considered that this is an open problem not only in statistics. My reflections come also, for example, when models are complex (like in the Structural Equation Modeling or in the Path Analysis). So, in general, the research offers a plethora of models for explaining y=g(f(x),errror) but, what is strong necessary is a hint (a test) that could suggest the right direction!!! I am curios to see who won the Kaggle challenge (and mainly how)!!!