fela

I think the best term would have been statistically surprising, because it strongly hint at the fact that the result would be surprising under the null hypothesis, witch really is all that "statistically significant" really means. Sometimes surprising results happen, but all other things being equal they might hint at the null hypothesis being false. I could also live with "statistically interesting". "Detectable", suggested in another comment, seems to have some of the same issues as significant, it is too strong and seems to imply that now we know something is really there.

I don't think this is true unless you have a ridiculously high electricity bill. When I checked, one intercontinental retour flight was roughly equivalent to my yearly electricity bill, in terms of CO2 emissions. I have to admit I'm not sure how to reconcile this with CO2 credit prices, but I'm quite sure it's not really possible to offset the CO2 emissions of a intercontinental flight with 20 euro, that would mean that a minor tax on flights would make them practically carbon neutral, this is definitely not the case.

I assume you meant: If an airplane is as safe as average then it has PUT_NUMBER chance of having 2 incidents after 150k flights. 0.01% is actually the number I'm getting, assuming parent estimates are correct and making naive assumptions. In other words only 1 every 10 000 airplane models will have 2 incidents that early on if they are of average safety.

That is different then stating the probability of it being as safe as the average airplane, which you can't do as easily without additional modelling/priors and bayesian statistics.

I like to split the theorem in the following way:

P(Hypothesis|Data) = P(Hypothesis) * evidence_factor

P(Hypothesis) is the prior probability of the Hypothesis being true, in other words the probability we gave to the Hypothesis before seeing any of the data we are using in the theorem. When new data is observed, we use Bayes' theorem to update our believe in the hypothesis, which in practice means multiplying our prior probability by a number that depends on how well the new data fits our hypothesis. More precisely:

evidence_factor = P(Data|Hypothesis)/P(Data)

So it is the ratio of how likely our data is if our hypothesis is true, compared to (divided by) how likely it is in general. If it is more likely to occur in our Hypothesis, our probability of it being true increases, if it is more likely in general (and thus also more likely in case our hypothesis is not true, you can prove mathematically that those two statements are the same), then our believe in the hypothesis decreases.

TLDR: Prob(Hypothesis after I have seen new data) = Prob(Hypothesis before I saw the new data) * (how likely I am to see the data if my hypothesis is true, compared to in general)

Don't you need time to even define movement? Movement is a change of the position with respect to time. So without time you can't have movement. But obviously you are right that the two concepts are strictly related, that doesn't mean time doesn't "exist" (however you define "exist").

But that is very interesting, that means that when saying the numbers they were basically using something similar to Arabic numbers!

The current stock price (and thus market cap) already assumes future growth. The market cap would increase further only if growth exceeds the current expectations of investors. (Or due to other factors unrelated to growth).

I stopped using bookmarks after I realized I wasn't using them, thanks to a combination of:

1. Autocompletion: for any website I use regularly I just write a substring of the url or Title (Firefox does this especially well). This covers probably 70% of my browsing.

2. Google. This might take slightly longer in case I want to find a specific article I had read some time ago, but it still seems less effort that having to bother with bookmarks, in my experience: either you have a very long list of unsorted bookmarks, in witch it's hard to search, or you have to spend time sorting them into sub-folders.

Now that I think of it, the following would be a very useful Google feature: +1 an url so that it becomes much more likely to bubble to the top in future searches.

Looks a bit like an over engineered coffee machine to me. On the other, if customers enjoy the experience, why not.

The definition of p-value is the same independent of method, as far as I can tell the only real difference is that by Neyman–Pearson you just look at whether the p-value is below a threshold, and Fisher looks at p-value as "strength of evidence" valuable in itself. It's still not the probability that your result was due to chance, it's the probability that under the null hypothesis (and you will definitely need one) you would get that value (or more extreme) by chance.

"it’s telling you that there’s at most an alpha chance that the difference arose from random chance. In 95 out of 100 parallel universes, your paper found a difference that actually exists. I’d take that bet."

This is wrong. It’s telling you that there’s at most an alpha chance that a difference like that (or more) would have arisen from random chance if the quantities are actually equal. And if the quantities are equal 95 out of 100 parallel universes would not be able to reject the null hypothesis.

Is he saying that he would take the xkcd bet[0] on the frequentist side?

[0] https://xkcd.com/1132/

"what are the odds that the results you observed could have arisen by chance?"

If you say it like this it will very easily be misinterpreted. Once your results are in there are two cases: (1) either the null hypothesis is true and you got those results due to chance, or (2) the null hypothesis is false and there was some actual effect outside of the null hypothesis that helped you get the results.

Due to this it is very easy to interpret you statement as referring to the probability of (1).

Two two following definitions of p-values sound similar but are not:

[Correct] The probability of getting the results by chance if the null hypothesis is true P(Results|H0)

[Wrong] The probability that you got the results by chance and thus the null hypothesis was actually true P(H0|Results)

I'm not saying you didn't get it, but somebody reading what you wrote can very easily be fooled. And there are a lot of dead wrong definitions on the web[0][1][2][3].

[0] https://www.americannursetoday.com/the-p-value-what-it-reall...

[1] https://practice.sph.umich.edu/micphp/epicentral/p_value.php

[2] http://natajournals.org/doi/full/10.4085/1062-6050-51.1.04

[3] http://www.cdc.gov/des/consumers/research/understanding_scie...

Unfortunately no. Very much no, even though it's widely believed that that is a good definition/intuition (and used in many places).

It's the odds of having that results due to chance, if the null hypothesis is true[0]. That latter part might sound pedantic, but the whole point is that we don't know how likely the null hypothesis is. If I test wheather the sun has just died[1] and get a p-value of 0.01 it's still very likely that this result is due to change (surely more than 1%)! We need a prior probability (i.e. bayesian statistics) to calculate the probability that the result was due to chance, that is why that partial definition is incomplete and actually very misleading. This point is subtle, but very important to really understand p-values.

Another way to look at it is: if we knew the probability that the result was due to chance we could also just take 1-p and have to probability of there actually being some effect, a probability that hypothesis testing cannot give us.

There is one nice property that hypothesis testing does have (and why presumably it's so widely used): if the idea you are testing is wrong (which actually means "null hypothesis true") you will most likely (1-p) not find any positive results. This is good, this means that if the sun in fact did not die, and use 0.01 as your threshold, 99% of the experiments will conclude that there is no reason to believe the sun has died. So hypothesis testing does limit the number of false positive findings. The xkcd comic is a bit misleading it this regard, yes it does highlight the limitations of frequentist hypothesis testing, but the scenario depicted is a very unlikely one, in 99% of the cases there would have been a boring and reasonable "No, the sun hasn't died".

For an incredibly interesting article about the difficulty of concluding anything definitive from scientific results I highly recommend "The Control Group is out of Control" at slatestarcodex[2].

[0] To be even more pedantic you would have to add "equal or more extreme", and "under a given model", but "if the null hypothesis is true" is by far the most important piece often missing.

[1] https://xkcd.com/1132/

[2] http://slatestarcodex.com/2014/04/28/the-control-group-is-ou...