## On consistency

In the wake of the Press Gazette "debate", I was watching an exchange of views on Twitter between BH reader Foxgoose and Andrea Sella, a University College London chemist who moves in scientific establishment and official skeptic circles.

Sella was explaining how persuasive he found the observational record of climate:

Think like a scientist! Temperature is only a proxy. Energy balance is real issue & C19 physics is alive and well.

Like Warren Buffett you mustn’t be affected by shorter term fluctuations.

As I said, don’t just look at surface temps. Look at sea level and global ice mass too. All part of same.

I gently inquired of Sella whether he there had been any statistically significant changes in these records, to which he responded:

1.56 ± 0.25 mm over a century isn’t significant?

I then pointed him Doug Keenan's one-page article about why you can't decide about significance just by looking at a graph.

This brought about the following rebuke from Richard Betts.

Your 'statistical significance' argument is silly: http://wmbriggs.com/blog/?p=8061

The link is to a Matt Briggs article on why statistical significance is a flawed concept. As readers here know, Briggs is a Bayesian and sees flaws in the frequentist approaches to statistics. This is fine, but frequentists will of course shoot back that there are problems that are as bad or worse with the Bayesian approach. I'm not enough of a statistician to come down on one side or other of this particular fence and I can cope with people making arguments under either paradigm.

But people do need to be consistent, a point Briggs makes in the article Richard B linked to.

If we seek to understand this physics, it’s not likely that statistics will play much of role. Thus, climate modelers have the right instinct by thinking thermodynamically. But this goes both directions. If we have a working physical model (by “working” I mean “that which makes skillful predictions”) there is no reason in the world to point to “statistical significance” to claim temperatures in this period are greater than temperatures in that period.

Why abandon the physical model and switch to statistics to claim significance when we know that any fool can find a model which is “significant”, even models which “prove” temperatures have declined? This is nonsensical as it is suspicious. Skeptics see this shift of proof and rightly speculate that the physics aren’t as solid as claimed.

This brings me neatly back to where we started. Andrea Sella points to the observational records and implies that I should draw conclusions from them. My response is that if you think we can learn something from them, show me how the change is significant. If you think statistical significance is a flawed concept and that we should be examining the congruence of observations with the output of physical models then do not wave temperature graphs in front of my nose. Tell the public loudly and clearly that we can learn nothing from observational records on their own and that we need a physical model. Then tell us why your physical model is sound despite estimating a value for aerosol forcing that is at material variance with observations, and despite it producing estimates of warming that vastly exceed observations.

And you absolutely must not, as the Met Office has done, tell the GCSA that warming is "significant" without any statistical foundation. Do not, as the Met Office has done, tell Parliament that warming has been "significant" without any statistical foundation either. Doing things like this will leave you having to beat an embarrassing retreat to a position of "we don't use statistical models", directly contradicting your earlier pronouncements. It will also leave you in the tricky position of having to explain whether you think the IPCC is "silly" for using statistical significance, or indeed whether your own employer is "silly" too.

## Reader Comments (92)

Isn't this the point that one of our noble lords(sorry, forgotten which one) made in the other place?

Do you really mean "official skeptic circles" in your first paragraph?

[BH adds: Yes - I'm referring to the Skeptic Society lot]

This debate on significance parallels the IPCC attitude on certainty that one timeyou can pick a 90% figure of the hat and then the next time you pick a 95% out of the hat, with no calculations visible, so demonstrates alarmist evangelists disrespect for statistical formalities.

- Climate science shows itself to be an utter shambles as no authority figure stood uo and shouted, instead they leave it to the small boys to say the king has no clothes.

Oh, perish the thought! Mind you, Richard Betts, for whom precision in posting is not exactly a demonstrated strength, does seem to have a penchant for making declarations via twitter that he later has to back down from. Unfortunately, this is rarely in the same forum where he made the original declaration, so his twitter followers are left in the dark regarding his subsequent retraction.

Then again, "silly" might mean something

completelydifferent in the lofty sphere of climate science. Maybe it's been redefined like ... oh, I dunno ... "trick", "decline", "fudge" - or Michael Mann's latest contribution, "exonerate" ;-)Andrew,

If you "can't decide about significance just by looking at a graph", and clearly are getting a handle on some of the issues about statistical significance, then why were you asking Sella the Chemist about the statistical significance of the supplied number?

By your own arguments, you should be asking about the practical significance of such a thing instead? Surely, you should follow your own advice and be more consistent? ;)

I was asking Andrea to explain why

hethought it was persuasive."Think like a scientist! Temperature is only a proxy."

What about those "scientists" that firmly believe in proxies of proxies?

"If your experiment needs statistics, you ought to have done a better experiment." Ernest Rutherford.

If this whole thing boils down to a bunch of obsessives arguing about whether you can see a change in a random walk graph, we ought to be wondering what we should be doing instead to resolve the issue, or preferably not to win or lose some abstruse argument, but to find the truth.

Or from another POV, if this is the playing field, wondering about models and significance, my null 'nothing much is happening' remains unchallenged by the CAGW hypothesis.

"Then tell us why your physical model is sound despite estimating a value for aerosol forcing that is at material variance with observations..."

I don't have any problem with your argument, but object to the phrase "at variance", which here means "doesn't fit". The sentence should say "doesn't fit".

Using the word "variance" in an article that contains references to statistics is confusing because "variance" is a technical term used in statistics which has a specific meaning. "Goodness of fit" is also a statistical term, but I think "fit" on its own would not be confused with any technical term.

You can excuse yourself for not being a statistician but at least pick up and read something like Statistics Made Simple to help avoid confusion in terms.

Andrew,

I don't think you've answered my point. He thought *what* was persuasive? Was it you or him that brought up statistical significance (as opposed to common-or-garden significance)?

Well some understand the significance of the global surface temperature record:- Ed Hawkins

It is deceptive to demand that people ignore the significance of a given change.

The main problem is that there is not enough data. Africa has 1000 odd weather stations. According to the WMO it needs 12000 to give near adequate data coverage. even if all land was adequately covered there is still the 70% oceans with no coverage.

Also to claim that rising sea levels points to climate change is a false claim since if all oceanic inputs were to stop the seas would still rise due to river feeds of sediment, erosion and plate tectonics.

Climates change, unfortunately the ''climateers'' think that it can onlt change by getting warmer. This is a poor analysis because since the climate is solar driven solar output falls give colder temperatures.

Doug

I'm saying that Andrea found the observational records persuasive.

If we are to draw inference from observational records without reference to a physical model, we need to consider statistical significance, right? Andrea was asking us to infer things from the observational record, so I was gently probing to see if he recognised this.

When you say "common-or-garden significance" what do you mean? If this is to say "temperatures have gone up" or "sea level has gone up", then we are back to a case of "So what?" - this was the point I was probing with my tweets to Andrea.

Ahem...actually temperature is a fundamental part of the energy balance equation:

Changes in heat storage = absorbed solar radiation - emitted terrestrial radiation

CE.∂Ts.∂t = 1-αp.S0^4-A↑

where, CE is the effective heat capacity of the media (measured in J/m^2/K),

Ts the surface temperature,

t the time,

αp the planetary albedo,

S0 the Total Solar Irradiance (TSI) and

A↑ the total amount of energy that is emitted by a 1 m2 surface of the Earth.

A↑ could be represented on the basis of the Stefan-Boltzmann law, using a factor τa to represent the infrared transmissivity of the atmosphere (including the greenhouse gas effect), as A↑=ε.σ.Ts^4.τa

reference:

http://www.climate.be/textbook/chapter3_node6.xml

Of course in the measured energy balance the error bars are larger than the signal so the argument is truly academic. ie If you don't look at the temperatures then there is nothing else to look at and certainly nothing to validate the models with - not that they ever seem to bother with model validation either.

So...think like a scientist my foot! More like make stuff up with no foundation and pretend it's a fact like a climate scientist.

I asked a few threads back what might be the explanation of any downward trend in global temperatures

beforethey occurred. It would appear that the answer will be that we have to look at energy balance. Looking at Sella's preferred metric, with no change in global sea ice for 35 years and the latest paper on sea levels showing a deceleration in trend, why wait?http://wattsupwiththat.com/reference-pages/sea-ice-page/

http://hockeyschtick.blogspot.co.uk/2014/03/new-paper-finds-global-sea-level-rise.html

And just to tie it up..

"..you mustn’t be affected by shorter term fluctuations."

Like the short heating period between 1979 and 1998?

"don’t just look at surface temps. Look at sea level and global ice mass too"

And discover that they are still perfectly normal?

"1.56 ± 0.25 mm over a century isn’t significant?"

No it isn't and of course 0.6K/century isn't either - by any measure you like.

These people just rely on a pessimistic gut feeling - not on physics.

Thinking like a climate scientist, there is no way the observational records can be removed from the discourse...people will like to see where things have been going to, plus a nice trend overimposed showing what the future will bring (usually, the trend is simply an extension of whatever has been happening in the last few years - "if it rains, forecast rain").

Energy balance chattering is particularly unpersuasive to the long-time reader of climate books. Any material produced on the topic during the last 50 years has invariably shown infographics where incoming and outgoing energy balance out.

Unfortunately, those same graphs have been changing, and will change in the future, so the impression is that there are many unknowns about energy fluxes, and people just change their figures in order for them to be balanced. IOW the infographics can tell us very little.

Thought that was worth repeating.

1.5mm of sea level isn't just insignificant, it's barely measurable!

1.56 ± 0.25 mm over a century is nothing. If one would like to use sea levels as a proxy to prove AGW:

- it should be flat in the beginning of 20th century.

- there should be an accelerated trend due to AGW.

The big problem with these "official sceptics" is that they are just cheerleaders of science. They are used to argue against creationism and homeopathy. They haven't done their homework to figure out what the fuss in climate science is about. They just assume that the scientists are again right and think that an attack against climate science is an attack against science. They couldn't be more wrong.

I think 'cheerleaders of apparent science' would be more accurate, Vieras.

"And you absolutely must not, as the Met Office has done, tell the GCSA that warming is "significant" without any statistical foundation."

No, as we now know courtesy of drive-by Doug, this is 'common-or-garden' significant. Not the same thing AT ALL.

And the amazing thing is that such 'common-or-garden' significance can only be detected, to 95% confidence, by the world's self-selected experts. So not really common but rather elite garden.

I wonder if the warming hand been ‘statistically significant’ if those sane people making the claim that the 'statistically significant’ concept is its self-incorrect would be sticking to this line. Or would they be shouting about how good the evidenced was and its now proved beyond any doubt ?

I think with all know the answer to that , as so often we seen how what is ‘proof ‘ depends solely on what supports or does not support ‘the cause’

Climate change science having opened its doors to Dana, Romm and Bob Ward it's unsurprising the experts appear better suited to farm^H^H^Hgarden work.

One issue that has come up when discussing the climate is whether certain events are statistically significant. That, in turn, raises a question: what does it mean for something to be “significant”? I have sometimes given a short explanation like this: an event is

significantif it is unlikely to be due to random variation, i.e. it is outside the range of what would probably occur due to natural variability. Some people have asked for elaboration on that. Some elaboration follows.The first thing that we need is the concept of a

statistical model. An example will illustrate the concept. Suppose that we have a coin. We toss the coin a few times, with the outcome of each toss being either Heads or Tails. We might then make two assumptions. First, the probability of the coin coming up Heads is ½. Second, the result of one toss is unaffected by the other tosses.A statistical model is a set of assumptions about the process that generates the data. In our example, the model would comprise our two assumptions. The set of assumptions does not have to fully describe the process. In our example, the assumptions do not tell us what type of coin was used, how long each toss took, or the path of the coin through the air. The assumptions, though, should be enough to allow us to analyze the data statistically.

The set of assumptions—i.e. the model—almost always differs from reality. For instance, our assumption that a coin comes up Heads with probability ½ is only an approximation. In reality, the two sides of a coin are not exactly the same, and so the chances that they come up will not be the same. It might really be, for instance, that the probability that a coin comes up Heads is 0.5000001 and the probability that it comes up Tails is 0.4999999. Of course, in almost all practical applications, this difference will not matter, and our assumption of a probability of ½ will be fine.

There is also another way in which our model of coin tossing is differs from reality. We can determine the outcome of the toss by measuring the position of the coin prior to the toss, measuring the forces exerted on the coin at the start of the toss, and determining the air resistances as the coin was about to go through the air (all this is in principle; in practice, it might not be feasible). Thus, the real toss is deterministic: it is not random at all. Yet we modelled the outcome of the toss as being random.

This second way in which our model differs from reality—incorporating randomness where the actual process is deterministic—is fundamental, unlike the first way. Yet, by modelling the outcome of a coin toss as random, our model is vastly more useful than it would be if we modelled the toss with realistic determinism (via all the physical forces, etc., that control the outcome of the toss). Indeed, statistics textbooks commonly model a coin toss as being random. Moreover, people have probably been treating a coin toss as random for as long as there have been coins.

To summarize, we model a coin toss as a random event with probability ½, even though we know that the model is not true. This exemplifies a maxim of statistics: “all models are wrong, but some are useful”.

Now suppose that we toss the coin 10 times and get Heads every time. Intuitively, that is a very improbable result. We can make that intuitive notion rigorous by calculating the probability of getting 10 Heads in 10 tosses. We determine the probability by doing a calculation—using the two assumptions that we made, i.e. using our statistical model. Doing that calculation, we can determine that the probability of getting 10 Heads in 10 tosses is less than 0.001. Such a low probability is very good evidence that the coin is not a fair coin.

Suppose instead that the coin was tossed only 3 times. If the coin came up Heads each time, we would not have good evidence that the coin was unfair: getting Heads 3 times can reasonably occur just by chance. Using our model, we calculate that the probability is 0.125.

The two probability calculations are both based upon our model. That is a crucial point. Every statistical analysis consists of two phases. The first phase chooses a statistical model for the data. The second phase draws inferences using the model. Inferences are always drawn from the model—rather than directly from the data.

Returning to our original question about the meaning of

significant, we have the following.The definition leaves open two questions. First, how low should the probability be? Second, how should the statistical model be chosen?

Regarding the first question, a common convention is 0.05. My opinion is that 0.01, or less, would be better.

Regarding the second question, this is arguably the biggest question in statistics. Indeed, one of the world’s leading statisticians, Sir David Cox, says the following, in his book

Principles of Statistical Inference: “How this translation from subject-matter problem to statistical model is done is often the most critical part of an analysis”.It is important to remember that the model is not reality. If we choose the model well, the differences from reality will be irrelevant—as with our coin-toss model. If we do not choose well, however, any inferences that we draw from the model might be seriously misleading. For instance, in choosing our coin-toss model, if we had assumed that the probability of the coin coming up Heads was ⅛, instead of ½, then we would have calculated that probability of getting 3 Heads in 3 tosses to be less than 0.002, and so significant.

The foregoing illustrates the principles of how we determine whether an event is significant. How do we apply those principles to events in the climate system? For example, global surface temperatures have risen by about 0.9 °C since 1880; is that rise significant?

Our first task is to choose a statistical model. What model should be chosen? With the coin-tossing example, the choice was obvious. For global temperatures, the choice is not obvious at all. For some discussion of this issue, see my critique of statistical analyses in the IPCC Fifth Assessment Report. My critique explains that we do not know enough about the climate system to choose a statistical model—and so, in general,

we cannot statistically analyze climatic data. This affects all the statistical analyses that have been done to date.A statistical model was chosen by the UK government in 2012 (see Parliamentary Question HL3050). That choice, however, was disputed by Lord Donoughue, and the government later effectively acknowledged that its chosen model was untenable: for details, see the Bishop Hill post Met Office admits claims of significant temperature rise untenable.

This issue has been pressed further by Lord Donoughue. As a result, on 21 January 2014, the government stated the following.

That ought to be the end of attempts to statistically analyze climatic data, at least in the UK. I suspect, however, the many people—on all sides of the global-warming debates—will continue to claim that they have done such statistical analysis.

If a statistical model for climatic data is chosen, it will have a random component—just as our model of a coin toss did. Note that the climate system is deterministic (ignoring quantum effects, which seems reasonable). When we do statistical analyses of climatic data, though, we consider portions of the model to be random—just as with our model of a coin toss. The random component is used to indicate what we believe will probably occur due to natural variability.

Returning to my original, short, explanation of

significant, that could be expanded as follows: an event issignificantif it is unlikely to be due to random variation in our chosen model, i.e. it is outside the range of what we believe would be reasonably expected to occur under natural variability.It should be clear that the question “is the warming since 1880 reasonably expected to occur under natural variability?” is extremely important. Answering that question statistically is essentially asking if the warming is significant.

Similar issues arise when consider the stall in temperatures, during the past 15 or so years. There has been much discussion about the explanation for the stall. If the stall would reasonably be expected to occur under natural variability, though, there might well be nothing to explain.

Finally, you might reasonably ask, if we cannot statistically analyze climatic data, what analyses should be done to study global warming? The answer is that we should use computer simulations of the climate systems.

Doug Keenan, isn't the probability of ANY sequence of heads and tails over ten tosses in fact the same? How could any one series be significant? How can a lot of weather all within the known variation be significant of climate change?

You don't need statistics to tell if anything out of the ordinary is going on. Although statisticians love this stuff, if anything were really happening we would not have to argue about it. Nothing much IS happening. Teasing significance out of it by methodological or model choice means in itself that is only a game. (The former applies to this climate debate only. I am not denying the applicability of stats to appropriate problems.)

Douglas J. Keenan

The answer is that we should use computer simulations of the climate systems.

Been there done that , and its not worked , which why they keep looking for that which may not be missing in the first place. So the honset approch may be to say , we can do that BUT its unlikley toallow us to make a prediction worth much more than saying tomrrow it may or may not rain.

But honset is not the same as 'effective' is it?

statistics is our interface to the observed world

We are not connected to thermometers via a neural necklace, we are not !

I find it "remarkable" that warmish Phd's would contend differently.

Their clowndance towards calorific thinking, after 20y+ hysterical alarmism about the UEA CRU temp anomaly, is very amusing.. :)

The City University debate was about journalistic ethics - that's why they had Bob Ward, Steve Jones and Fiona Fox on the panel!

And they didn't see the irony.

What is going on at UCL?! There was a time that they taught thermodynamics fairly well. If someone showed up at UCL and said 'I've created a calorimeter which is the size of the earth and I am going to monitor it with a couple of thousand thermometers and a few tree rings', I do hope that the would be laughed at...!

rhoda:

This reminds me of a conversation I had a few years back with a well-connected journalist lady who was born within 12 months of myself. She was totally convinced that climate had been changing significantly in our lifetime and gave examples of the kind of thing. (I can't even remember what but spring coming earlier, the latest floods or drought, whatever.) And I was thinking: of course things had changed but it wasn't significant, certainly not in terms of justifying. as she thought, massive attempts to decarbonise (a link to Michael Kelly's very important thoughts via the GWPF today). And at once I thought of Roger Pielke Jr and his mastery of the appropriate

statistical methodsto analyse such trends. Otherwise we're prisoners of fruitless subjectivity forever.I don't have a problem with Doug Keenan's last point about simulating climate using software as being our only option per se. It's how we verify that we're on the right track that seems highly problematic. Not any old software kludges will do, to put it mildly.

The sentence I found more potentially misleading, at least for the unwary, was:

Speaking as a pure scientist or statistician maybe. But not for the man in the street in his 4-by-4 or the policy maker thinking of pricing him out of that priviledge. Necessary but not sufficient is I think the appropriate qualifier in that case.

I should finish by saying thanks to Doug for such a clear exposition.

I am quite fond of significance tests. First of all because I laboured mightily to make sense of the concept, and secondly because in practical situations it can be useful to have some kind of an assessment of the strength of evidence in some data for some particular notion of interest. The flaw is that the conditions for strict applicability of a particular test are not liable to be met easily, and so a certain wooliness creeps in. That wooliness might be relatively minor, and can sometimes be checked for and improved upon. But for practical purposes, we must remember that inductive logic is a messy business compared with the elegant certainties of deductive logic. In that messy area, we can benefit from even modest help, and that modest help is what significance tests can provide. Another benefit, is that they can encourage disciplined data gathering and analysis and help encourage a firm determination not to be fooled by any data into unwise decisions no matter how convenient they may be. But if the tests are misunderstood, for example if someone supposes they are about proving or disproving hypotheses, then they can bring delusion or oversight into play. They are merely about assessing the weight of evidence in a particular data set for a particular hypothesis. As Briggs has noted (see http://wmbriggs.com/blog/?p=9338), p-values can be small whether or not the Null Hypothesis is true. But that misses the point if you are not concerned with proving or disproving the Null. In general, we know the Null Hypothesis is false, and we don't need any data at all on that! For example. it is clear to me that our adding CO2 to the atmosphere will have some effect on, amongst other things, temperature. My Null Hypothesis might be that it has had no effect at all. Zero. Zilch. I 'know' that is wrong, but I use the artificial device of the Null to assess the strength of evidence in a temperature record by computing, on the assumption that the Null is true, what kind of excursions that data set could be expected to display in some computed statistic say 99% of the time. If my real data set shows an excursion of that statistic beyond these, then I have a statistically significant result at 1%. That's good evidence that something is going on, and helps me estimate the both the magnitude and direction of it. But note that it does not disprove the Null, nor does it prove the Alternative. I have merely got what looks like a decent piece of evidence to work with.

According to my impressions of Doug Keenan's analyses, the temperature records or constructions such as global mean temperature, he has looked at are consistent with a null hypothesis of business-as-usual, of no change. This does not mean that there has been no change. It does not mean he has 'proved' the null. It merely means that these temperature records, by themselves, are not very convincing evidence that a particular change, or even mere direction of change, has taken place. If that was all the evidence you had, for example, you might not want to threaten your economic prospects as a country, nor scare the wits out of your schoolchildren, with dire stories of doom and gloom, nor force upon everyone associated prescriptions as to how we should lead our lives and view the future.

Betts and his colleagues are playing games with the lives of the poor people of the UK and he sees nothing wrong with that as long as he can continue to rely 100% on his models. REMEMBER, his job depends on them.

Some very heavy stuff in these posts - not sure I follow it all. But my version would be to observe that the smaller the change in the measured variable the greater will be the impact of background or random or accidental variations. For example, I completely concur with jamesp's approach that the tiny changes in sea levels are at best insignificant and at worst not measureable. We have tidal ranges of over 10 meters twice a day all around the UK with huge variations being influenced by numerous influences of varying magnitude from gravitational pull to minor changes in air pressure. What is actually being measured? If its mean sea level that is an imaginary concept with no precision at all. The Rutherford quotation is apt - if advanced statistics are needed to interpret a change there is something wrong with the data.

Statistics in climate science is even more a minefield than Doug Keenan suggests.

If we had for 20 days in a row with the same maxima and the same minima all over the globe, that would be a clear outlier, a portentous phenomenon of climatic change despite being a very clear example of no mathematical change at all.

The SREX authors were nicely aware of the issue.

Stephen Richards: Characteristically you overstate the case and thus damage the case. Richard Betts I'm sure has never advocated that we "rely 100% on his models". Likewise it's ridiculous to suggest that his job depends on that.

Of course Richard's views are affected by the job he does but he wasn't in this case out of order to point to the Briggs blog post which criticises Keenan significance. Let's take care to play the ball, not the man - especially in cases where the attack on the man is obviously wrong and thus reduces the credibility of other people's more effective criticisms of a smug consensus.

Smashing argument, Bish. On the matter of "garden variety significance," isn't that the same thing as "importance?" In other words, when saying that something is significant the meaning is that it is important.

Yes, Theo, raising the inevitable question: important to whom? Value-laden as they say.

Richard Drake

I have been looking for an appropriate collective noun to describe people

who appear to be bereaft of reason within the climate debate.

I have arrived at the term "Amygdalanians"

This term was inspired by Daniel coleman and in particular, his 1996 book

"Emotional Intellegence"

He introduced the term "Amygdala Hijack"

What do you think?

Hmm, I think I need to read up on the Amygdala hijack but it looks a fruitful line of inquiry. Should we perhaps do a discussion thread called 'Psychological models'? I've been thinking about something more general than just bashing Dr Lew. Ah yes, stewgreen already has Psychology of Climate belief/dis-belief. Anyway up to you, thanks for the suggestion - I'm sure others will benefit as well as me!

Richard Drake

Thanks for that.

I am going to try and construct an article to support the term based on the nature of the

amygdala (deep seated part of the brain) and its ability to distort the information which

it receives from all our senses.

It's only a theory of course but if I can capture in words what is circulating in my aged brain

then I will risk making a complete fool of myself.

Oh, risk making a complete fool of yourself. Some of us need company :)

I would like to improve upon my reported impressions of Doug Keenan's work on this. I have just revisited the paper he links to above (his critique) and it is quite clear that his view is that since no statistical time series model has been identified by the IPCC or the Met Office for the analysis of atmospheric temperature records of interest over timescales of interest, then it is impossible for them to report a valid significance test for changes. They therefore cannot claim statistical significance. This is materially different from my supposition at the end of my previous post, but my concluding thoughts retain some force. In the absence of a valid statistical significance analysis, would you want to do those things based on temperature records alone?

@ rhoda, 2:18 PM

Each individual sequence is indeed equally probable. There is only 1 sequence with 10 Heads, though, whereas there are 252 sequences with 5 Heads; thus, sequences with 5 Heads are 252 times more probable than the sequence with 1.

@ Richard Drake, 2:59 PM

So you agree that it is necessary, but you do not agree that it is important‽

Ah yes, the good Bishop ventures into red Queen territory here. Eli has already dealt with this with his flock reduced to throwing spaghetti against the wall and hoping that something sticks leading to claims that every one of a set of mutually contradictory papers are just wonderful.

As another said many non-scientists have no clear idea of how highly rated redundancy is in science. You don’t really believe anything seriously before it has come from several independent sources. And those sources themselves are often internally redundant, like surface temperatures, monthly averaged, correlate over long distances. Same with replication: I can replicate with the best of them someone else’s coding errors by running their code. Independent replication, by different people, using their own code and methods, on different data (if you can get it) proves something.

Doug, sorry if I wasn't clear. Your original was:

First, I was agreeing that this is an extremely important question for a scientist, aided by the best statistical understanding and methods. Second, even if it were to be shown that the warming since 1880 (or 1950) could not reasonably be expected to occur under natural variability, this would not in itself spell imminent doom. It would not necessarily imply that the pace of decarbonisation must be greatly increased through policy making. It would be necessary but not sufficient for that. What would be sufficient for that? That's a genuinely difficult one.

Doug, yes if you think order does not matter. Sometimes it does.