Editing Talk:2110: Error Bars
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Good explanations but if I understand the comic correctly, the article does not really get to the point. It is indeed true that different modelling assumptions will give different confidence intervals, but a more mundane and more important source of uncertainty is statistical error (e.g., sampling error). CIs are typically used to convey the uncertainty around a point estimate (e.g., a mean) which has been computed from a random sample. If you take another random sample from the same population (e.g., perform an exact replication of an experiment), you will get a different mean, but also a different CI. See Cumming's dance of p-values and CIs for an illustration: https://www.youtube.com/watch?v=5OL1RqHrZQ8, or a talk I gave that covers a larger range of statistics: https://www.youtube.com/watch?v=UKX9iN0p5_A. In my talk I explain why it doesn't make sense to report inferential statistics (p-values, CIs, etc) with many significant digits, because you could have easily obtained very different p-values or CIs. The belief that inferential statistics are "stable" across replications is a very common misconception that can easily lead of erroneous inferences. So if you care about your statistical analyses being interpreted correctly, it is tempting to show the uncertainty around all the inferential statistics you report, including CI limits, as Monroe is suggesting. Like any statistics, CI limits are a function of the data and thus have a sampling distribution (https://statmodeling.stat.columbia.edu/2016/08/05/the-p-value-is-a-random-variable/). Thus you can estimate the standard deviation of this sampling distribution, and this gives you the standard error of the confidence limit. There is one inaccuracy in the comic (I think): you can't define CIs on CI limits, because there is no true population value of CI limits. However you can compute standard errors of CI limits, or alternatively prediction intervals, and then compute standard errors and prediction intervals again and again, recursively. If my explanation makes any sense I can try to summarize it and incorporate it in the article. [[User:Dragice|Dragice]] ([[User talk:Dragice|talk]]) 10:47, 13 February 2019 (UTC) | Good explanations but if I understand the comic correctly, the article does not really get to the point. It is indeed true that different modelling assumptions will give different confidence intervals, but a more mundane and more important source of uncertainty is statistical error (e.g., sampling error). CIs are typically used to convey the uncertainty around a point estimate (e.g., a mean) which has been computed from a random sample. If you take another random sample from the same population (e.g., perform an exact replication of an experiment), you will get a different mean, but also a different CI. See Cumming's dance of p-values and CIs for an illustration: https://www.youtube.com/watch?v=5OL1RqHrZQ8, or a talk I gave that covers a larger range of statistics: https://www.youtube.com/watch?v=UKX9iN0p5_A. In my talk I explain why it doesn't make sense to report inferential statistics (p-values, CIs, etc) with many significant digits, because you could have easily obtained very different p-values or CIs. The belief that inferential statistics are "stable" across replications is a very common misconception that can easily lead of erroneous inferences. So if you care about your statistical analyses being interpreted correctly, it is tempting to show the uncertainty around all the inferential statistics you report, including CI limits, as Monroe is suggesting. Like any statistics, CI limits are a function of the data and thus have a sampling distribution (https://statmodeling.stat.columbia.edu/2016/08/05/the-p-value-is-a-random-variable/). Thus you can estimate the standard deviation of this sampling distribution, and this gives you the standard error of the confidence limit. There is one inaccuracy in the comic (I think): you can't define CIs on CI limits, because there is no true population value of CI limits. However you can compute standard errors of CI limits, or alternatively prediction intervals, and then compute standard errors and prediction intervals again and again, recursively. If my explanation makes any sense I can try to summarize it and incorporate it in the article. [[User:Dragice|Dragice]] ([[User talk:Dragice|talk]]) 10:47, 13 February 2019 (UTC) | ||
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