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Comment by try_the_bass | Hacker News Reader

> Freedman's latest calculation, which incorporates data from both the Hubble Telescope and the James Webb Space Telescope, finds a value of 70.4 kilometers per second per megaparsec, plus or minus 3%.

> That brings her value into statistical agreement with recent measurements from the cosmic microwave background, which is 67.4, plus or minus 0.7%.

Does it? As a lay person who can do basic arithmetic, this seems incorrect? Maybe there is some rounding or truncation, since I didn't check the source paper, or maybe I don't understand how confidence intervals work.

`70.4 × 0.97 = 68.288` and `67.4 × 1.007 = 67.8718`

These numbers are certainly close, but to my naive interpretation, the ranges don't overlap?

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> These numbers are certainly close, but to my naive interpretation, the ranges don't overlap?

As is typical, the tolerances given are sigma values for an assumed normal distribution, not the width of a uniform distribution. The disagreement is less than five sigma, so (in the domain of physics) the disagreement is not considered significant enough to be a high-confidence indicator of new physics.

This wins some kind of award for most useful information packed into two sentences on HN. This is exactly what I've been wondering since this came out.

This is a big source of confusion when it comes to errors. I think most people think intuitively in terms of a 'peak-to-peak' specification of errors, i.e. range of X means that all possible values are within that range. But that's not really how statisticians think, and they tend to think in terms of standard deviation. Even if you soften the 'intuitive' view to 95% confidence range, that's about a 6x difference in terms of what the number means (assuming, optimistically, a gaussian distribution).

It looks like "statistical agreement" is doing a lot of work in that statement.

Not really. You can calculate the statistical significance of the difference of these measurements, which I’ve done here: https://www.mycompiler.io/view/4LA310YXZHO

For a null hypothesis of “their differences are consistent with zero”, the p-value is 17%, equivalent to a 1.4 sigma difference. That’s pretty far from a reasonable rejection criterion for the null hypothesis. I think most people would agree that that means these measurements are plausibly consistent.

it is "c" divided by the age of Universe for pretty obvious reasons. Now we just have to precisely determine the age of the Universe :)

Nothing about this is obvious. The age of the universe is related to the integral over the inverse Hubble parameter. The age of the universe is founded by measuring the Hubble constant among other things, not the other way round.

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