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mercoledì 13 maggio 2020

The importance of confidence intervals


Anyone taking a basic statistic course learns what a confidence interval is. For the uninitiated, it is a range of plausible values ​​(with a fixed probability) that are obtained when estimating something with a statistical model/method.
These intervals play an extremely important role in understanding whatever phenomenon is being studied statistically. They tell us a story about risk. In fact, they consider the amount of available information  (sample size) and the potential variation of the estimate in the reference population. So they tell us in what interval the real answer can fall. They are therefore like a large warning sign placed above any estimate, warning to treat with caution the single number produced by the point estimate. They say "attention, you can't be more accurate than that, the observed (or predicted) reality moves from a minimum of x to a maximum of y".

If you have to make a decision based on some estimate, you need to look at how big this interval is, you have to know what the level of confidence is (and therefore its complement, the error),  all this becomes fundamental to prevent possible disasters.

Let's think a moment about what are the implications of ignoring a confidence interval (I don't consider it or I don't calculate it properly). I am a public decision-maker, I get a number from a model (statistical or not), for example, the number of ICU admissions following covid19 for the next day. Based on that number I have to decide whether to rush to open new beds or take another precautionary measure. I only have a number, perhaps not very high, I trust who produced it and therefore I assume it is precise. All right I go to sleep peacefully. Then in the middle of the morning, the head of the most important city hospital calls me saying that he no longer knows where to put the cases requiring intensive care ... ups. If instead of that single number I had received a range of values, which tells me with very high probability (99%) that the interval between x and y will contain the true number of hospitalizations, and y is greater than the capacity of my intensive therapies, I'd rush to take measures, because the risk of finding myself with saturated intensive care is very high.



But even in less dramatic situations, if I have to make a decision based on estimates, numerical models, and/or assorted simulations, having the opportunity to evaluate their reliability with some criterion, better if an interval, will allow me to save me and others in thousands of situations.

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