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1 vote

Estimating mean and SD given the median and IQR values

The long answer is "no" this is not possible to determine without additional information about the distribution of the data. The pragmatic answer is "yes", if you make assumptions ...
Gregg H's user avatar
  • 5,564
1 vote
Accepted

Non-parametric one-sample mean test for a bounded variable (based on Chebyshev's inequality?)

I think for this there are several well known concentration inequalities that can be applied. In particular Hoeffding, Azuma, and McDiarmid. Not that there's any real difference between the bounds one ...
MotiNK's user avatar
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4 votes

Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

The misinterpretation of confidence intervals is related to what Blitzstein and Hwang (in their probability textbook) call "sympathetic magic". Sympathetic magic is an anthropology term for ...
Abhishek Divekar's user avatar
3 votes

Non-parametric one-sample mean test for a bounded variable (based on Chebyshev's inequality?)

Here is a maximum likelihood approach. Suppose you have $n$ observations of $X$ which total $T$, and you want to test the null hypothesis $E[X]=\mu$, with $T/n<\mu$. Then the maximum-likelihood ...
Matt F.'s user avatar
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1 vote
Accepted

Why can the standard error of the weighted mean be smaller than the standard errors of the individual measurements?

The short answer, as @LulY pointed out in the comments, is that you now have a larger combined sample size. Take the standard error of the mean for example: $$\mathrm{SE} = \frac{s}{\sqrt{n}}$$ Larger ...
Frans Rodenburg's user avatar
1 vote

Why can't the slope be greater than 1 in regression to the mean for married couples' intelligence?

The slope of a linear regression is $$\text{slope} = \rho \cdot \frac{sd_y}{sd_x}$$ If we assume $sd_y \approx sd_x$ and $\rho<1$, then $\text{slope} < 1$. See also the question: Effect of ...
Sextus Empiricus's user avatar
2 votes

Why can't the slope be greater than 1 in regression to the mean for married couples' intelligence?

I interpret Kahneman as saying that you don't need to resort to theories about women marrying down if the correlation between husband and wife IQ is imperfect. But I suspect he was not precise in ...
dimitriy's user avatar
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1 vote

Why can't the slope be greater than 1 in regression to the mean for married couples' intelligence?

I think you are plotting the wrong thing. If you look at a fit of wife_iq vs. husband_iq, then we could well get a slope of 1, or less than 1, or more than 1. But what Kahnemann says is that highly ...
Peter Flom's user avatar
  • 125k
0 votes

Under what conditions are there pairwise monotonic relationships between mean, variance, and (positive) skewness of a lower-bounded distribution?

It turns out there is a lower bound on the skewness of any strictly positive data set having given mean and sd: $$ g_1 > \sigma/\mu - \mu/\sigma. $$ This doesn't seem entirely consistent with your ...
David C. Norris's user avatar
0 votes

Variance around true value, not mean

yes you can, if you do you may use the whole sample size as the denominator (n instead of n-1, as you aren't using any degree of freedom for estimating the mean), however, you may get a bad result if ...
carlo's user avatar
  • 4,555
4 votes
Accepted

Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript

If $X \sim \operatorname{Normal}(\mu, \sigma^2)$ then $Y=e^X$ has a log-normal distribution with the same parameters and $X=\log(Y)$. So you simply need to take logarithms and exponentiation ...
Henry's user avatar
  • 40.5k
6 votes

Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript

A log-normal variable is normally distributed in the log scale, so the identity holds in the log scale. To set the scene, let's review the normal case first. The $p^{th}$ quantile $Q(p)$ is calculated ...
PBulls's user avatar
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