Do parallel universes effect my t-test results

Question

I rolled a dice 20 times and got 6 each time. I thought the chance of this happening by chance is very low, so it is probably likely something is behind this like perhaps the dice is bias. But then i thought if there are infinit universes, it is very likly this could just happen by chance, then maybe i am just that person that happen to get 20 6's by chance. Then i thought if I think like this all my t-test results i produced for drugs trials also mean nothing. In fact nothing means anything.

Should we think like this? Should i say there is something significant behind my dice or its just happened by chance as we have infinit parallel universes. And if we say its just chance then how can we say anything is significant in drugs or vaccine trials.

I am a biologist not physists/mathmatitian, so go easy on that

Answer 1

There's no need to introduce parallel universes for this question. Although there's also no problem with thinking that way if it helps you -- sometimes when we talk about the results of an experiment probing a random variable like a dice roll, we imagine a hypothetical "ensemble" of experiments, which is similar to a set of parallel universes each of which has a different realization of the experiment.

Anyway...

You are right that rare outcomes will happen. If you roll a dice enough times, you will find a string of 20 dice rolls each of which is 6. Therefore if you roll a dice and find a string of 20 6's, you cannot conclude with absolute certainty that the dice are rigged. This is not special to your dice experiment; it is a fundamental limitation of observational science that we always have some uncertainty in our observations.

However, we can quantify the uncertainty that we have. If you do roll 20 6's in a row, you can ask how likely you were to observe this outcome. The probability of rolling a 6 with 2 dice is $5/36\approx 0.14$, and therefore the probability of rolling 20 6's in a row is $(5/36)^{20}=7.1 \times 10^{-18}$. Needless to say, this is quite unlikely.

Now you have to be careful how you interpret this number. It means that, if the dice are not rigged, you have a extremely small chance of observing 20 6's. It does not mean that the dice are definitely rigged; it does not mean the probability that the dice are rigged is $1-7.1 \times 10^{-18}$; it does not mean that the probability of there being parallel universes is large or small. However, it does mean it would be a bad idea to place any bets that are based on the assumption that the dice are fair; I wouldn't bet that the next dice roll would be a 7.