One of the biggest issues non-scientists tend to run into with sets of data is the difference between correlation and causation. If you search, there are other sites which have covered this topic, in some cases probably better than I will. Most non-scientists default to causation (it’s actually multiple different fallacies). The thing is, our brains are trained to look for connections, and may then manufacture connections when none actually exist. If you search for ‘correlation fallacy graphs’, you find some very interesting results, such as this website.
For the most part, unless you’re a conspiracy theorist, you look at these results and think “well, that’s ridiculous. There’s no way these things are connected”—and you are (probably) right. But there are much less ridiculous and still completely unconnected things we think are connected all the time, only because they occur in more proximity (washing your car or watering the lawn and it starting to rain, for example), they don’t seem as ridiculous.
On the whole when we find ourselves thinking something obviously caused something else, we should examine our assumptions. Every time something like that happens, to stretch our critical thinking we should try to construct the logical argument behind such an occurrence. How, theoretically, would we get from A to B, if they really are logically connected? What would the steps required be?
Where a writer is concerned, being aware of fallacies like these is an important step. Like learning the rules of grammar, it’s important to learn the rules of logic. Like a quote attributed to Picasso: “Learn the rules like a pro so you can break them like an artist.” If you’re going to include a run-on, do it deliberately, for effect, for the story. If you’re going to include a fallacy, you want it to add to, not detract from, the story. If you’re aware of fallacies like this, you can use them to control the readers’ expectations. You can include two events that aren’t actually connected as a red herring. Just be aware that there are trade-offs. While it most certainly makes the story more realistic (sometimes, bad things just happen through the sheer power of chance, or things happen that aren’t connected at all), if incorrectly handled it may also tick off some of your readers for having read it wrong.
You should generally have an idea why things happen, even if you have to figure it out after the fact (you’re just writing, going with the flow, and afterwards decide whether or not to keep it in your story based on whether it actually fits and accomplishes the objectives you wanted it to). Is it a random happenstance? Does one cause the other (and if so, is it opposite of the original assumption of cause and effect)? Are both related to an entirely different source? Is it coincidence? Is it some sort of more complicated system that’s not simply cause and effect, but actually involves multiple factors leading to an outcome?
Where have you run into assumptions that just because two things have happened, that they’re related? Did they make sense in-story (such as in the case of magic or horror stories), or did the writer just include the fallacy without seeing whether it makes sense?