# Summary

To be clear, these statistical tests are imperfect for drawing absolute conclusions about the concomitant variation between two variables (see, for example, Resnick, 2019). However, as they are those that best understood and currently available, these are the methods used.^{[1]}

Concomitant variation is just one of the critical attributes required in the attempt to establish a causal relationship exists, that is, the extent to which one variable has an influence on another. The others attributes of causation being: 1. A logical/theoretically sound reason for one factor to influence another, 2. That the hypothesized influencing factor changes before the one it is expected to influence, and 3. There are no other variables that better explain the effect (see Boyd, 2020) and that the research is ‘parsimonious’ (see, also, Aarts, 2007). And remember, concomitant variation alone does not show that one variable influences the other. As the perennial *research & analysis* warning emphasizes: Correlation (alone) ≠ Causation!

Establishing this concomitant variation, that the value of the dependent variable, is indeed influenced by the independent variable, is a statistical process based on probability theory. You don’t really need to understand the math to understand the process (as described above). What you do need to know is 1. Which statistical test is appropriate in which situations and 2. How to tell the extent to which the test confirms such a relationship.

The appropriate statistical test is determined by the type of variable for the independent and dependent variables (*Categorical* or *Numeric*). The extent to which the relationship is confirmed is assessed through the ‘Significance’ level of the test. Most researchers typically use the .05 threshold, meaning that if the result (showing a relationship) was unlikely to be arrived at purely by chance, then it may have occurred because there was, in fact a relationship. That is, values less than .05 (e.g., .022) suggests that the relationship was, quite possibly, truly established.

- Apologies here to anyone trained in Statistics and/or Research Methodology. Largely avoided here, except in a few footnotes, are the critical mathematical processes for deriving the mentioned statistics. There is also no real notion of hypotheses or the formal process of hypothesis testing, Type I or II Errors, or descriptive inferences. Given the intended audience, the necessity for brevity and that the paper is part of a series on the determination of ‘cause-and-effect,’ univariate tests have been skipped. And the biggest faux pas was intentional; there was only tangential mention of the Null Hypothesis. Better a little slightly incorrect understanding, than none at all. ↵