• If you’re a psychology researcher investigating possible causes of depression (Y), you may have trouble disentangling the effects of poor sleep quality (A) and anxiety (B), both of which tend to be correlated with depression.
• If you’re a health researcher investigating the causes of diabetes (Y), you may have trouble disentangling the effects of high carbohydrate intake (A) and obesity (B).
• If you’re investigating the causes of high life satisfaction (Y), you may have trouble disentangling the effects of friendship quality (A) and mental well-being (B).

In all these examples, we know that at least two of the variables (A and B) are related to the main variable (Y), but the really tricky question is to figure out what all the possible causal relationships are between the three. For instance, does A cause B, which causes Y, does Y cause both A and B, or is there some other explanation? 

In the pdf below, I sketch out 45 possible explanations to consider in situations where there are two variables that both correlate with a third variable of interest.

First of all, there are the types of causal relationships one often expects, where A and B both cause Y in simple ways (either directly or through each other):

Even if A and B really do cause Y, they could be interconnected to each other in complex ways:

It also could be the case that only A or only B causes Y, with the other variable only appearing to cause Y due to a confounding effect:

It’s also possible that Y is actually one of the causes rather than merely being caused by A and B:

Then there are situations where there is a critical other variable (or set of variables – represented as a “?” below) that are integral to the causal structure:

Finally, there are situations where Y is caused by A or B (or both), but Y also causes A or B (or both), resulting in a cyclic relationship:

Here’s a link to my pdf showing most of the possible relationships.

If you want to read about other challenges associated with untangling causality in the real world, you can read another post about this here.

I first created this diagram on April 19, 2021. I made minor edits to the diagram and wrote this piece with assistance from Clare Harris. This piece first appeared on my website on November 22, 2023.

The first step is to admit to yourself that you’ve made a mistake. Trivial errors, like accidentally putting the container of orange juice in the freezer, are easy enough to come to terms with. But for more serious matters, or matters that involve pride or shame, our minds often recoils at the pain caused by acknowledging we’ve screwed up. We make up excuses as to why it isn’t our fault, or pretend (even to ourselves) that it didn’t happen. But remember: refusing to accept that we’ve made a mistake frequently dooms us to making many more in the future. I find that reflecting on this fact helps me acknowledge my own mistakes. Another thing that can help is to remember that mistakes are not weird, they are the norm. The best among us still make them frequently.

Occasionally, noticing mistakes is enough to correct them, especially when they have immediate reinforcing consequences. Put your hand in a fire once, and it will be easy not to do it again. Get stung by bees enough times, and you’ll likely become more wary around bees. But if you don’t consciously reflect on what has happened, you may not learn all there is to be learned from your mistake. Worse still, many mistakes don’t lead to natural self correction.

Step two is to generalize from your mistakes so that you can see the pattern or principle underlying them. The lesson derived from the mistake of sticking your hand in fire shouldn’t just be to not stick your hand in fire, it ideally should include not sticking your hand in boiling water too. The principle to extract is that objects of high temperature can be dangerous to touch. If your friend is upset because you didn’t return his call for a month, the lesson to learn may not just be to return calls more quickly with this friend, or even just to return calls more quickly with all your friends. Considering this mistake in the context of your other mistakes, there may be something deeper that you should also learn. If you’re having trouble figuring out what, try discussing your mistakes with others whom you trust not to be judgemental. They may be able to offer a perspective that hasn’t occurred to you.

Step three is to develop a strategy to change your behavior. Just because you know that you should stop forgetting to pay your friend back for dinner doesn’t mean that you will stop forgetting. And it certainly doesn’t mean that you will start being more responsible in general when you owe something (even if you’ve made that mistake many times). What would stop your forgetting? Maybe emailing that friend right now to make lunch plans, and putting a reminder in your calendar software saying “bring the money you owe!”, set to go off just before you leave to meet that friend for lunch. Problem solved. How do you solve the more general problem of being bad about paying back what you owe? One approach that might help is to try to build a habit of always scheduling calendar reminders as soon as you borrow money to remind you (repeatedly is best) that you need to pay the money back. That way it is much harder to forget.

Step four is to review your big mistakes, as well as the principles you’ve extracted from them and the strategies you’ve developed to change your behavior. If you review these from time to time you’re much more likely to actually change. Just because you learned something from a mistake three months ago doesn’t mean you’re going to remember what you’ve learned three months from now. As unnatural a thing as it may seem to do, keeping a list which you review from time to time will dramatically magnify your ability to retain what you’ve learned.

So the next time you realize you may have made a mistake:

1. Acknowledge it, if it was indeed a mistake. Otherwise you may be doomed to repeat it.
2. See what useful principles you can learn from it, taking into account the context of the other mistakes you’ve made.
3. Develop a strategy to change your behavior. Just willing yourself to do things differently next time often doesn’t work. Figure out what you can do now to alter your future behavior.
4. Keep a list of your big mistakes and what you should learn from them. Review this from time to time (for instance, whenever you add a new mistake to the list).