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Could someone explain what this implies? As a non-mathematical person who sometimes uses these tests in biological experiments, I find it frustrating why stati

• Tloewald 11y ago
  The beginning of the article discusses common fallacious interpretations of confidence intervals (i.e. what most of us probably naively think a confidence interval means, e.g. 10 ±2 95% means there is a 95% probability that the true value is between 8 and 12). The authors then go back to basics and explain what a confidence interval actually is (that, on average, experiments conducted the way this experiment was would have had a 95% chance of capturing the correct value inside the interval -- a subtle but important distinction). Then they create a neat example which shows how four different approaches to calculating confidence-interval-like-things work in practice. Then they go into technical details I couldn't be bothered reading. Finally, they suggest that bayesian "credible intervals" do a much better job of providing what people intuit a confidence interval to be. As someone trained in classic statistical methods who has not had occasion to really use Bayesian methods, one of the things I like about Bayesian approaches is that they seem much more real world and practical to me. E.g. most statistical analysis tools assume a bunch of ridiculous and impossible things (e.g. that you do not look at the data until it has all been collected; that every time you look at the data you need to add a "degree of freedom" meaning that looking at the data 10 times produces 10 increasingly less reliable results -- literally NO-ONE does this and yet it is crucial for the theory to work.) The Bayesian approach is more like "as you get data, make and refine estimates of what the data means" which is how we actually do things, and so -- everything else aside -- we aren't violating the approach's base assumptions every time we use it.
  • lacksconfidence 11y ago
    > had a 95% chance of capturing the correct value inside the interval I'm still not clear on this, what does it mean? I also tried to read the linked text but it's quite dense and drawn out.
    • Tloewald 11y ago
      The experiment has already taken place and its findings are either correct or incorrect. It's not a Schrodinger's Cat, the Cat is alive or dead. Imagine two studies have been completed and they have non-overlapping confidence intervals each of 95%. Does each have a 95% chance of having captured the result? Obviously not -- at most one may be correct.
  • pcrh 11y ago
    Thanks! I'm glad to know I had the correct interpretation of confidence intervals!
    • Tloewald 11y ago
      Well, assuming I got it right :-)
• brendano 11y ago
  I find it frustrating why statisticians can't just give us something we could indeed use with confidence that it actually tells us what we think it tells us... This is on a slightly different statistical methodology issue, but quoting from Brad Efron (http://statweb.stanford.edu/~ckirby/brad/papers/2005BayesFreqSci.pdf http://statweb.stanford.edu/~ckirby/brad/papers/2005BayesFre...): The physicists I talked with were really bothered by our 250 year old Bayesian-frequentist argument. Basically there’s only one way of doing physics but there seems to be at least two ways to do statistics, and they don’t always give the same answers. This says something about the special nature of our field. Most scientists study some aspect of nature, rocks, stars, particles; we study scientists, or at least scientific data. Statistics is an information science, the first and most fully developed information science. Maybe it’s not surprising then that there is more than one way to think about an abstract subject like “information”.
  • pcrh 11y ago
    Thanks, that was an interesting read!