Timeline for Mean absolute deviation (MAD) analogy to 68-95-99 rule
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 12 at 10:49 | comment | added | Peter Flom | Playing around with @jcken 's code, with a uniform distribution (0 to 10) I got 50% within 1 MAD, 99% within 2 and 100% within 3. With an exponential distribution, rate = 1, I got 50, 81, and 88. | |
| Jun 2, 2022 at 7:04 | comment | added | status | Easiest is to see why I asked it. To me, the math behind 68-95-99 rule is a bit complex. I looked at proofs, would be capable of understanding more of it, but since mean absolute deviation is 50% and not 68%, I thought maybe it relates to a probability distribution in an easier way. Was I thinking it had to be normal distribution. No, just if there was some analogous common relationship. Where maybe 50%, x%, y%, were mathematically more easy to get. It was just very basic question. | |
| Jun 1, 2022 at 12:45 | comment | added | whuber♦ | The title clearly is asking for an analogy and so does not imply any interest in Normal distributions or even approximately Normal distributions. Moreover, the 68-95-99.7 rule holds far more generally than Normal distributions. | |
| Jun 1, 2022 at 6:58 | comment | added | jcken | Further experimentation suggests the result of 50% laying within $\pm 1 \text{MAD}$ only holds when the underlying distribution is continuous. Using the data generating distribution as poisson(1) gives $\approx 36%$ within $\pm 1 \text{MAD}$ of the median | |
| Jun 1, 2022 at 6:48 | comment | added | jcken | @whuber I agree; however the reference to the 68-95-99 rule in the title implies OP was interested in the Normal distribution. @status; you should consider updating your question to be clearer about what types of distributions you want to learn about. For example, Pukelsheim's 3$\sigma$ rule tells us that under quite weak assumptions, at 95% of values lie within $\pm 3 \sigma$ of the mean jstor.org/stable/2684253 - I am unaware of similar results that use MAD but there may be something out there | |
| May 31, 2022 at 23:08 | comment | added | status | Wuhber, if you read what I wrote, I suggested I might not be assuming normal distribution. Jcken likely built on Dave’s comment. I appreciate what Jcken contributed so far. | |
| May 31, 2022 at 21:05 | comment | added | whuber♦ | There's something a little oxymoronic about this approach, because someone employing MAD likely is concerned that the data are not Normal. Under the assumption of Normality they also would more likely just convert the MAD into an estimate of SD by multiplying it by about 5/4 (approximating $\sqrt{\pi/2}$) and then proceed to apply the 68-95-99.7 rule. | |
| May 31, 2022 at 19:59 | comment | added | status | Thanks, good idea to simulate it. I usually do so when I can’t understand it from the math directly. If I meant that normal distribution should be assumed, well, I don’t know. Is normal distribution derived from standard deviation being assumed, or does it not matter much if MAD is used instead? Mostly I was thinking there might be some obvious pattern where data falls off in a way that is intuitively easy to get. 68-95-99 isn’t super intuitive, it uses some error function of 1/sqrt(2), etc. | |
| May 31, 2022 at 19:08 | history | answered | jcken | CC BY-SA 4.0 |