This is probably easy for you

[Sailr]

I am not a statistics person. A friend of mine and I were chatting over a beer and were trying to figure the following problem out. Given our lack of knowledge on statistics, we ultimately agreed that we were both useless when it came to figuring it out. Here it is.

A given problem or hypothesis contains 100 interrelated variables.
You believe your measurement that determined the value of each variable is 99% accurate. (Assume all values are weighted equally, to keep this simple.)

What is the probability that, when you add these variables together, you will reach the correct conclusion?

if the variables are not weighted equally, but you are still 99% confident in each variables measurement, does this lessen or increase the probability that your outcome will be correct?

We both believe that the probability the correct answer will be reached is less than 99% and think that 1% of uncertainty across 100 different variables is significant, but we don't know what the probability actually is or how you would calculate it.

I apologize in advance if I am not using the correct statistical terms to pose this question. Can someone help us get to the correct answer?

Thanks!

[Dason]

Are we assuming that if you get two measurements wrong that they won't cancel each other out to give the correct measurement? If this is the case then all we're looking at is the probability we got all the measurements correct right?

[Sailr]

Hi Dason,

Thanks for helping us out.

Your understanding is correct with regard to two measurements not canceling each other out. Basically, if you were 100% confident in your 100 measurements and understanding of the interrelationship between the variables, then, on a simplistic level, you could say that you have 100% probability of being correct. On the other hand being off by just 1% on each of 100 variables would seem to haver the potential to give you a wildly different outcome.

On a simplistic level, one example we came up with is boiling water. if you believe with 99% confidence that it boils at 178.2 degrees, but you are off by 1% and it actually boils at 180 degrees, then that 1% error in your prediction would make a noticeable difference in the outcome. Another layer to add to that would be the heat transfer efficiency of the pot it is in. The less efficient it is, off by 1% for example, the more it will impact the desired outcome of boiling water. Another potential layer would then be the purity of the water itself, and on and on. Our expectation is that when you have a complex system with 100 interrelated layers, that small 1% variance significantly lowers the likelihood that your predicted outcome will be correct.

Hope that helps