Day 30: Confidence Interval
Day 30 already! Where does the time go? It feels like we just started this whole project and it probably wouldn’t be a good idea to look at the remaining time to completion, so let’s not and just enjoy the nice round 30. We will get back to our p.d.f another day, but today is going to be short. That’s what I usually say before typing out 10 pages worth of information so to avoid that, let’s touch on something important, but something I can do briefly. Today we’re talking about confidence intervals*
Last post we talked more about our p.d.f. and C.D.F and we actually even covered confidence interval, but if you blinked you may have missed it. Because we want to have a good foundation to build from we should probably define what exactly a confidence interval means!
When we want to perform any sort of statistical tests, such as the one we did three posts back, we need to define an interval we want to evaluate. In that post we had several that we looked at. One of questions we posed was what were the odds that our value x fell between 0 and 0.5. We did the math and saw that we had a 25% chance of having our value x fall in that range.
Now here is the subtle bit, what we did when we asked what the odds were that our value would fall between 0 and 0.5 was create our confidence interval. That is to say that our confidence interval is between 0 and 0.5 and we have a 25% chance that our x value will fall in that range. That is what a confidence interval means, it is the range of data that has an associated probability.
Remember, there was nothing special about where we selected our confidence interval, we could have asked what the chances were that our value x would fall between 0.5 and 1 or 0.3 to 0.6. The takeaway here is that we are the ones to selects our confidence interval. In the case of our example it was the range we integrate from (0.5 to 0), which made the math super easy (for the example anyway, we saw a much more complex pdf earlier in the post).
That’s it! See short, but it is important to have working definitions of things, especially as we move forward. Next up we will probably dive into some other pdf functions since a certain writer is memorizing several for a class. I’ll let you work out the odds that it is this writer.
Until next time, don’t stop learning!
*My dear readers, please remember that I make no claim to the accuracy of this information; some of it might be wrong. I’m learning, which is why I’m writing these posts and if you’re reading this then I am assuming you are trying to learn too. My plea to you is this, if you see something that is not correct, or if you want to expand on something, do it. Let’s learn together!!