Accuracy and Intervals
Join Chris and Fred as they discuss how terms like ‘accuracy’ and ‘intervals’ … and how they are used in reliability engineering to help us measure the uncertainty we have in some concept. This came from a question we were asked …
… is it more accurate to use a 99 % confidence interval or a 90 % confidence interval?
This is a difficult question to answer! But lets try:
- What is ‘accuracy?’ This is a term that we have all used since we were young children. This is great! And perhaps not so great at the same time. When it comes to statistics, many of the terms we have used for much of our life actually means something subtly different when it comes to statistics. But let’s stick with ‘accuracy’ representing how ‘close’ some value is to a ‘true’ or ‘perfect’ value.
- So what is a ‘confidence interval?’ A confidence interval represents a region where we are reasonably confident that some value lies. For example, we might be able to say that we are 90 % confident that a randomly selected human’s height is between 5′ 4″ and 6′ 5″. We might also be able to say that we are 99 % confident that a randomly selected human’s height is between 5′ 0″ and 6′ 8″. Both these confidence intervals are ‘true.’ But neither one is more ‘accurate’ than the other. Confidence intervals help represent our confidence on some measurable quantity. Not the measurable quantity itself.
- But we often focus on parameters and not the data. Let’s say that instead of focusing on the actual heights of human beings, but want to study the average human heights. As we get more and more data, we can become increasingly confident about what we think the true average is. We can never find that value … unless we measure every single person in the world. So our 90 and 99 % confidence intervals we have on our understanding of the human heights will get smaller and smaller. Which is good.
- And bringing it back to accuracy? Accuracy is different to confidence. In some ways. Confidence is a state of mind. As we become more and more confident, the accuracy in our estimates and predictions based on that confidence becomes more accurate. Does this help?
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