Someone wrote to me about a diary they had kept for the past eight years about their dreams. About every other month or so, a dream of theirs came true. I was asked if I could quantify the likelihood of successful predictions.
Assessing psychic phenomena is outside my area of expertise, but I offered a few general suggestions, partly because I thought that an analogy to diagnostic testing was interesting.
Generally, it is almost impossible to quantify the success rate of predictions in dreams in any rigorous fashion. You could start by first turning the problem around. How often do you have a dream whose prediction does not come true? The advantage of this approach is that with dreams, the "hits" are more memorable than the "misses". By estimating a false positive rate, you force yourself to objectively evaluate both the "hits" and the "misses".
Even if you get a false positive rate, though, it is unclear how to interpret that number. If that number is exactly 100% then you have an easy interpretation: your dreams are worthless as a predictive tool. But what if that number is smaller than 100%? How much smaller does it have to be before we chalk it up to more than coincidence?
In medical testing, we evaluate predictions all the time--it is called diagnostic testing. This is an imperfect analogy because diagnostic tests are not predictions about the future, but rather predictions about events that are otherwise hidden from our view. Still, the analogy is useful. Evaluation of a diagnostic test requires specifying four numbers. The first is the number of true positives. In your situation, these are events that occur and which are predicted by your dreams. For example, you dream that your brother has a car accident and the next day he crashes his car into a parked car. According to you there are about 6 per year times 8 years or 48 true positives. Then there are the false positives. These are events that do not occur but which are predicted by your dreams. You dream that your brother has a car accident and he drives safely for the entire day following your dream. You don't state how often these occur, but if we presume that you have a dream that makes a prediction every other day, then you would have about 180 per year times 8 years or 1,440 predictions. 48 are true positives, so the remaining 1,392 are false positives. If it is every other week, then you have 24 per year times 8 or 192 predictions and 144 are false positives. The third number is false negatives. These are the events that occur and which are not predicted by your dreams. Your brother crashes his car and your previous night's dream gave no indication that this might happen. I hesitate to even guess at this number (how good a driver is your brother?). The fourth number is true negatives. These are events that do not occur and which your dreams predict will not occur. Your brother drives safely all the day long and nothing in your previous night's dream indicated a crash of any kind.
Furthermore, the criteria that are typically used for deciding whether a dream is a false positive are highly subjective. For example, you dream that your brother is in a car accident. If your brother is not in a car accident in the next 24 hours is the dream a false positive? Or do you expand the time window and say that the dream is a false positive only if your brother avoids a car accident in the next 7 days. What constitutes a "car accident". Does your brother have to be the driver or is he considered to be in a car accident if he is a pedestrian and another car hits him. Does a car smashing into his parked car while your brother is inside his house count? How about a large door ding? The false positive rate for your dreams changes depending on how broadly you define an accident. It is further compounded by the fact that your dreams predict different things at different times. So if your dreams also sometimes seem to predict family illnesses, you have to come up with an objective criteria for what constitutes an illness.
There's a cute story about this. Linus Pauling actively promoted the use of massive doses of vitamin C during the last few decades of his life. He believed it could cure just about anything from the common cold to cancer. During one interview he explained that after he and his family started taking Vitamin C supplements, they never had colds. The interviewer was a bit surprised probed a bit further "No colds? Ever?" Linus Pauling responded, "Oh just an occasional sniffle."
There are also dreams that fail to make a prediction of any kind. Do you have an objective rule for deciding which dreams represent predictions of the future and which dreams just represent pleasant events with no predictions in them at all? </p> <p>The problem with even a carefully crafted diary is that it is impossible to objectively assign each dream to one of the four categories (true positive, false positive, false negative, and true negative). An interesting experiment could be done if you find five other similarly detailed diaries from perfect strangers. Show the five diaries plus yours to a close friend. Make sure that any any obvious identifying variables like names and cities are removed first. Ask that friend to pick out which of the six diaries mirrors your life most closely. categories.
It is hoping for too much but if your dreams by chance involved a consistent quantitative element, like the closing figure for the following day's Dow Jones average, then it's easy to run some statistics. </p> <p>Barring that, I think the best you can hope for is an informal opinion, and you can get that from just about anyone. There is a mistaken belief that if the informal opinion comes from a professional statistician, it carries more credibility, but we statisticians are no better at this task than anyone else.
If you want to pursue this further, you should do some research into this. You should focus your efforts on what the skeptical community writes, because this represents a standard of evidence that you need to provide to convince an outsider that your dreams are unusual. A good starting point is the Skeptic's Dictionary by Robert Todd Carroll.
There are several active processes that you need to control for like confirmation bias, subjective validation, and post hoc hypotheses, and until you are aware of these terms mean, you will not be able to produce credible evidence.
The temptation is to go instead to a website of those who actively promote dream divination, but in my experience, these individuals rely heavily on informal evidence and anecdotes. You don't really need help developing an informal evaluation about your dreams; in fact, you've probably already done an informal assessment and want something more rigorous.