[Almaviva]

"The calculations put chance of the piracy having occured due to natural variability at 0.5%. “So it’s 99.5% that it occurred due to warming over the industrial era,” said Best."

We need to train children in school to understand what statistical confidence means, so that we stop saying wrong things like this.

[acover]

Why is it wrong?

If you reject the null hypothesis with a 99.5% chance it is not a type 1 error.

[Para2016]

You can't say it's 99.5% due to global warming alone though. You can say 0.5% occurring by random chance but you can't just ascribe everything to one causal factor. Could be multi-factorial.

[interurban]

While the exact language in the quote is perhaps implying something, it only directly says the that the cause is warming during the industrial era. It doesn't provide any direct information about causal factors.

[Para2016]

In the article: "So it’s 99.5% that it occurred due to warming over the industrial era," said Best.

I don't have a problem with them saying for example - "We believe that the river changed due to warming over the industrial era"

I don't really have a problem with anything they conclude to be honest, I was just answering another guy's question. Shitty of HN users to give me negative points over it. I feel like I'm on Reddit again.

[acover]

That is possible. However in the abstract the author states

"Based on satellite image analysis and a signal-to-noise ratio as a metric of glacier retreat, we conclude that this instance of river piracy was due to post-industrial climate change."

[Sniffnoy]

P(A|B) was swapped with P(B|A).

[acover]

The statement should be there is a 99.5% chance that we correctly rejected the null hypothesis.

I agree it isn't careful wording. Thanks.

[Almaviva]

I played a game of Monopoly where I started with a roll of 12. There was a 97% chance I correctly rejected the hypothesis that the dice were fair. Maybe this is true in some sense? But it's still somewhere between misleading and nonsensical to say.

[drt1245]

I think a better analogy is that it's like having many pairs of dice, and rolling each pair in turn until you get a roll of 12. Then concluding "this particular pair of dice must be loaded".

Presumably, the researchers did not select rivers at random to study, they selected this river in particular because of the changes it is undergoing.

[acover]

Yes, I agree that p-value tests have flaws. If you look at the data to determine your hypothesis it's easy to overfit.

Bayes factor appear to solve this issue. I disagree that this is a basic education issue. It is a lack of agreement among scientists as to what statistical analysis is appropriate.

[Almaviva]

"So it’s 99.5% that it occurred due to warming over the industrial era"

There are at least a couple of statistical fallacies in this conclusion. And there isn't a lack of agreement about that.

One problem with p-value tests is precisely that people misunderstand what the p-value means, which is where basic education comes in. It could save people from believing a lot of things they shouldn't. (Like many health and fitness crazes over the last generation, for instance) Or at the very least, we could train science journalists.

[gertef]

Your second sentence should be in quotation marks to clarify that your comment is debunking it.

[Sniffnoy]

...as best I can tell, you have still swapped them? It sounds like you're still talking about P(null hypothesis|evidence), whereas p-values are about P(evidence|null hypothesis). (Well, not quite the latter but something like it.)

[acover]

Yes. Ugh. You are right.

I treat P(evidence | null hypothesis) equivalent to P(null hypothesis | data). When it should be

P(evidence | null hypothesis) = P(null hypothesis | evidence) * P (evidence) / P (null hypothesis)

As we don't know either of those extra terms we can't determine P(null hypothesis | evidence).

Thanks.

Interestingly wikipedia notes that P(Reject H | H) = pre-defined threshold for rejecting H [1]

[1] - https://en.wikipedia.org/wiki/P-value

[Almaviva]

> Why is it wrong?

https://xkcd.com/882/

If you look at 200 rivers, it would not be surprising to find something that naturally occurs 0.5% of the time. It is not correct to say that there is a 99.5% chance that this is due to non-natural causes.

[archgoon]

The wording is ambiguous. In general, trying to determine whether a statement about probability is correct or not requires more information than can be encapsulated in a single sentence. The English language does not help in this.

We're not going to get more information here without someone looking into where the .5% number comes from.

[acover]

Here is the statistical analysis from the paper:

The method of Roe et al. is summarized as follows. Let 1L be the change in glacier length over the past 130 years (∼1.9 km), and let σL be the standard deviation of glacier length due to stochastic fluctuations in mass balance, b, from natural, interannual climate variability. The signal-to-noise ratio is defined by sL =1L/σL . Likewise, sb =1b/σb . Ref. 12 demonstrates that the two are related via sL =γ sb , where γ is an amplification factor that depends only on the duration of the trend and the glacier response time, τ . The probability density function (PDF) for sb is generated by combining the signal-to-noise ratios of the observed melt-season temperature and annual-mean precipitation trends, normalized by the summer (bs) and winter (bw ) mass-balance variability (Supplementary Fig. 1a,b,c), respectively. We take σbw = 0.3 myr−1 and σbs =0.5 myr−1 , based on the observed mass-balance variability at Gulkana Glacier and the analysis of the global datasets of glacier mass balance33. The glacier response time is given by τ =−H/bt , where H is a characteristic glacier thickness, and bt is the (negative) net mass balance at the terminus. We set H=590 m, based on the scaling relationship for glacier geometry suggested by Haeberli and Hoelzle34 and measured cross-sections35; and we set bt =−7 myr−1 , estimated by extrapolating the vertical mass-balance profiles calculated by Flowers et al.8 , thus giving a central estimate for τ of ∼80 years. A PDF is estimated assuming τ follows a gamma distribution incorporating a broad uncertainty of στ =τ /4 (Supplementary Fig. 1d). The PDFs for γ and sb are combined to give a PDF for σL from the relation σL =γ 1L| obssb . This, in turn, is used to evaluate the null hypothesis that 1L| obs occurred due to natural variability. Supplementary Fig. 1e shows our estimate that there is only a 0.5% chance that the observed retreat of Kaskawulsh Glacier happened in the absence of a climate trend.

[Almaviva]

The 0.5% quote is fine. It's turning it into a 99.5% that is not fine.

It's essentially like saying that a pair of dice that rolled a 12 has a 97% chance of being loaded, because there's only a 1 in 36 chance of rolling that high.

[archgoon]

Let's think about this.

Let's assume that when a river gets redirected, a scientist goes and investigates it (which seems reasonable), and is asked what is the chance that it happened by natural causes, or is due to global warming. Based on the analysis that @acover shared with us, we can see that out of a thousand such dispatches, 995 will be due to global warming and 5 will be due to natural variability. So it seems correct for that scientist to conclude "It's 99.5% due to global warming.". In fact, saying that it's .5% due to natural variability is equivalent.

You are probably thinking of the jelly bean situation, where a test is performed to detect something within a sample population. The test has a failure rate, and the population has a base rate of occurrence.

In this case (thanks @acover), they are directly calculating the base rate.

Now, you could also ask "How many times in a year will a scientist be dispatched and be wrong", which is a again a different question (and is closer to the scenario you described).

[acover]

You could be right that we are only looking at variations that are rare. I'm not an expert so I would give the scientists the benefit of the doubt.

The possible error you identified is with the original paper and not due to a lack of basic statistics education.

[burntrelish1273]

Definitely.

Another good idea is to show the difference between reality and data can be overwhelmingly significant.

Videos demonstrating this with examples:

- "The Bayesian Trap" https://youtu.be/R13BD8qKeTg

- "Is Most Research Wrong?" https://youtu.be/42QuXLucH3Q&