Your aim of causality would start from your research design- an experimental design where you will have a proposed treatment or intervention, a control group an an experimental group. You may choose quasi experiment (non-inferential) or true experiment (inferential). If you opt for true experiment, you have a lot of choices (in addition to determining the descriptive means and difference between the means)- pretest-posttest, posttest only, Solomon four group, etc. Designs for these will need t-test of difference from independent samples, t-test of mean difference between dependent samples (or Z test), one-way ANOVA, t-test of relationship.
Causality is not directly computed. It is indicated by the difference in the mean scores (observed results) between the control group and experimental group (in post test only), and between the control group and experimental groups with different treatments or treatment levels.,
On the basis of this design and the data that you collect, you can now input accordingly your data to SPSS, Excel, Minitab, for the calculation of "causality".
What Eddie describes to me seems to be correlational which is not causality. To prove that X causes Y all else must be exactly replicated, including the environment, between your control and experimental groups and only 1 variable manipulated. If a change in Y is then reflected with a change in X then you can say the change in X caused the change in Y. Otherwise the changes in both were correlated.
Of course, correlation is not causation. The computation involves numerical data, no xperiment. Data have been collected already. The question is: how to proceed.
As far as I did not understand which kind of "numerical data" you intend to use to test for causality (I guess you are working with time series), I would suggest you to start trying if the package "Var" (or alternatively lmtest) included in the software R best fits your needs. It basically performs two different types of tests: an F-type Granger-causality test and a Wald-type test, which "is characterized by testing for nonzero correlation between the error processes of the cause and effect variables".
If you are studying causal relationships between time series, you should use the Johansen cointegration approach or the ARDL cointegration Bounds testing technique before applying the Granger causality tests. The best Software for doing that is to use Eviews.
Sofía: la elección de la técnica depende de la naturaleza de la situación, el tipo de estudio. el tipo de datos, la relación causal propuesta, la circunstancia de obtención delos datos, el tipo de variable y el dominio del misma, entre otras