I hope you realize that’s not how courts work. Seriously. In most developed countries, you are given the presumption of innocence. That is, you are assumed to be not guilty unless the prosecution can prove beyond reasonable doubt that you are guilty. The burden of proof is on the prosecution. You never really prove innocence.
Statistical testing works the same way really. We have a default assumption we call the null hypothesis (“not guilty”) and we collect data to see if we can prove the alternative hypothesis (“guilty”).
For example, if we are doing an experiment, and seeing if a factor is significant, the null hypothesis, or default assumption, is that the factor is not significant. We assume this, unless the data shows that the factor really is significant. How to do we determine this? By the p-value. The p-value is affected by the experimental noise, the number of samples we collect, and how much of change the factor seems to make on the output.
So what if we want to prove beyond a reasonable doubt that a factor is NOT significant? This has to do with the statistical notion of “power”. We will deal with that in a separate blog. But for now, as you might guess, it has a lot to do with sample size and experimental noise. And “noise” has to do with variation reduction in your process.
So as the old guy said, “turn that noise down!”