Timeline for Can I use 'mean ± SD' for non-negative data when SD is higher than mean?
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| May 10, 2023 at 11:40 | history | edited | mkt | CC BY-SA 4.0 |
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| May 9, 2023 at 13:49 | comment | added | Silverfish | Thanks for incorporating the feedback! (+1) As your answer mentions both SD and SE, it may be worth mentioning that mean ± SD is ambiguous. Same notation is used for mean ± SE or even mean ± 1.96 SE. Surprisingly common for people to say mean ± X without saying what X is! Re using quartiles as an alternative summary: in some fields it's absolutely standard/required to give descriptive stats for all variables in your dataset. Often in a huge summary table, with mean±SD for symmetric data, and median and IQR (or SIQR) if skewed. I much prefer quartiles myself but doesn't seem to be standard :( | |
| May 9, 2023 at 8:29 | comment | added | mkt | Fair points, all of you, that was sloppy of me. @Silverfish I've edited my answer to address this. | |
| May 9, 2023 at 8:28 | history | edited | mkt | CC BY-SA 4.0 |
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| May 9, 2023 at 7:52 | vote | accept | JIN | ||
| May 8, 2023 at 22:14 | comment | added | Silverfish | I'm a bit puzzled by this answer: "standard deviation is typically shown to convey information about uncertainty" seems like it should say "standard error" (which wasn't the question), unless it means "uncertainty about what the next observation from this distribution look like" rather than "uncertainty about the estimated parameter". While showing a plot is almost always a good idea, I don't think it obviates the need for an appropriate numerical summary. For highly skewed data, as this seems to be, I've often seen it suggested to quote median and quartiles or IQR instead of mean$\pm$SD | |
| May 8, 2023 at 19:35 | comment | added | whuber♦ | @cdalitz Thank you for clarifying. CIs were first mentioned in this answer, so really I should have been responding to mkt for assuming the OP's objective was generally to provide a description of confidence (presumably in the estimate of the mean). One usually reports an SD to give some sense of the spread in the data, which is only indirectly related to uncertainty in the mean. | |
| May 8, 2023 at 19:22 | comment | added | cdalitz | @whuber Sorry, this was confusing (and I am admittedly still confused, too). Neither IQR nor mean +/- SD yield an approximate CI for the mean. From the OP's use of "mean +/ SD" I concluded that he was looking for a description of the data distribution, not for one specific moment of the distribution. But this may just be a wrong interpretation of the question. I will add a comment to the question that asks for clarification. | |
| May 8, 2023 at 16:06 | comment | added | whuber♦ | In all fairness to @cdalitz, I think the phrase "this method" refers to sophisticated bootstrapping and not to confidence intervals generally and most would agree the former can be challenging for many audiences. But it would be problematic to substitute an IQR for a CI: that is a truly terrible procedure! After all, with increasing sample sizes the IQR will converge to--well, the population IQR, evidently; while any CI should shrink to a point with sufficiently large samples. Obviously, then, these two procedures reflect entirely different things and cannot be meaningfully interchanged. | |
| May 8, 2023 at 14:16 | comment | added | mkt | @cdalitz I don't agree. Readers don't need to fully understand the methods involved in calculating a confidence interval to comprehend what they mean. If that's where we set the bar for ourselves, we've effectively declared that statistics and science communication is impossible - even to other scientists! | |
| May 8, 2023 at 13:12 | comment | added | cdalitz | In the general sitution, confidence intervals are only obtainable via bootstrap (BCa bootstrap, e.g.), and , what's worse, this method is difficult to convey to someone without a degree in statistics. I would suggest to simply report upper and lower quartile and IQR (the difference between both). | |
| May 8, 2023 at 12:59 | history | edited | mkt | CC BY-SA 4.0 |
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| May 8, 2023 at 10:09 | history | answered | mkt | CC BY-SA 4.0 |