Basil Copeland and I also found linkages between surface temperature and solar cycles in two articles we published in the last year. We were roundly criticized and ridiculed by warmists mainly due to a statistical error in the first essay, but the base premise remained and the second essay was improved due to that error. I’m pleased to see that NCAR has found other solar to earth linkages, such as this one in ENSO. This is exciting news, but by no means a complete solution to the climate puzzle. There is much more to be learned about this. This is but one connector of the hydra-like patch cable that Dr. Jack Eddy imagined – Anthony
Scientists find link between solar cycle and global climate similar to El Nino/La Nina. Credit: NCAR
Establishing a key link between the solar cycle and global climate, research led by scientists at the National Science Foundation (NSF)-funded National Center for Atmospheric Research (NCAR) in Boulder, Colo., shows that maximum solar activity and its aftermath have impacts on Earth that resemble La Niña and El Niño events in the tropical Pacific Ocean.
The research may pave the way toward predictions of temperature and precipitation patterns at certain times during the approximately 11-year solar cycle.
“These results are striking in that they point to a scientifically feasible series of events that link the 11-year solar cycle with ENSO, the tropical Pacific phenomenon that so strongly influences climate variability around the world,” says Jay Fein, program director in NSF’s Division of Atmospheric Sciences. “The next step is to confirm or dispute these intriguing model results with observational data analyses and targeted new observations.”
The total energy reaching Earth from the sun varies by only 0.1 percent across the solar cycle. Scientists have sought for decades to link these ups and downs to natural weather and climate variations and distinguish their subtle effects from the larger pattern of human-caused global warming.
Building on previous work, the NCAR researchers used computer models of global climate and more than a century of ocean temperature to answer longstanding questions about the connection between solar activity and global climate.
The research, published this month in a paper in the Journal of Climate, was funded by NSF, NCAR’s sponsor, and by the U.S. Department of Energy.
“We have fleshed out the effects of a new mechanism to understand what happens in the tropical Pacific when there is a maximum of solar activity,” says NCAR scientist Gerald Meehl, the paper’s lead author. “When the sun’s output peaks, it has far-ranging and often subtle impacts on tropical precipitation and on weather systems around much of the world.”
The new paper, along with an earlier one by Meehl and colleagues, shows that as the Sun reaches maximum activity, it heats cloud-free parts of the Pacific Ocean enough to increase evaporation, intensify tropical rainfall and the trade winds, and cool the eastern tropical Pacific.
The result of this chain of events is similar to a La Niña event, although the cooling of about 1-2 degrees Fahrenheit is focused further east and is only about half as strong as for a typical La Niña.
Over the following year or two, the La Niña-like pattern triggered by the solar maximum tends to evolve into an El Niño-like pattern, as slow-moving currents replace the cool water over the eastern tropical Pacific with warmer-than-usual water.
Again, the ocean response is only about half as strong as with El Niño.
True La Niña and El Niño events are associated with changes in the temperatures of surface waters of the eastern Pacific Ocean. They can affect weather patterns worldwide.
The paper does not analyze the weather impacts of the solar-driven events. But Meehl and his co-author, Julie Arblaster of both NCAR and the Australian Bureau of Meteorology, found that the solar-driven La Niña tends to cause relatively warm and dry conditions across parts of western North America.
More research will be needed to determine the additional impacts of these events on weather across the world.
“Building on our understanding of the solar cycle, we may be able to connect its influences with weather probabilities in a way that can feed into longer-term predictions, a decade at a time,” Meehl says.
Scientists have known for years that long-term solar variations affect certain weather patterns, including droughts and regional temperatures.
But establishing a physical connection between the decadal solar cycle and global climate patterns has proven elusive.
One reason is that only in recent years have computer models been able to realistically simulate the processes associated with tropical Pacific warming and cooling associated with El Niño and La Niña.
With those models now in hand, scientists can reproduce the last century’s solar behavior and see how it affects the Pacific.
To tease out these sometimes subtle connections between the sun and Earth, Meehl and his colleagues analyzed sea surface temperatures from 1890 to 2006. They then used two computer models based at NCAR to simulate the response of the oceans to changes in solar output.
They found that, as the sun’s output reaches a peak, the small amount of extra sunshine over several years causes a slight increase in local atmospheric heating, especially across parts of the tropical and subtropical Pacific where Sun-blocking clouds are normally scarce.
That small amount of extra heat leads to more evaporation, producing extra water vapor. In turn, the moisture is carried by trade winds to the normally rainy areas of the western tropical Pacific, fueling heavier rains.
As this climatic loop intensifies, the trade winds strengthen. That keeps the eastern Pacific even cooler and drier than usual, producing La Niña-like conditions.
Although this Pacific pattern is produced by the solar maximum, the authors found that its switch to an El Niño-like state is likely triggered by the same kind of processes that normally lead from La Niña to El Niño.
The transition starts when the changes of the strength of the trade winds produce slow-moving off-equatorial pulses known as Rossby waves in the upper ocean, which take about a year to travel back west across the Pacific.
The energy then reflects from the western boundary of the tropical Pacific and ricochets eastward along the equator, deepening the upper layer of water and warming the ocean surface.
As a result, the Pacific experiences an El Niño-like event about two years after solar maximum. The event settles down after about a year, and the system returns to a neutral state.
“El Niño and La Niña seem to have their own separate mechanisms,” says Meehl, “but the solar maximum can come along and tilt the probabilities toward a weak La Niña. If the system was heading toward a La Niña anyway,” he adds, “it would presumably be a larger one.”
Source: National Science Foundation (news : web)
h/t to Leif Svalgaard
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Paul Vaughan (12:53:46) :
Paul, one thought about cycle length as that the length of the minima matter too, for timing and strength of el nino. That in turn is going to have an effect on the sampling of SST’s, and the curves we get. There’s a relationship between solar cycle amplitudes, outgoing longwave radiation, global temperature, and Stephen’s poleward expanding air circulations. I’m half way to understanding it. It may help with the phase reversal thing, at some timescales at least.
http://climatechange1.files.wordpress.com/2009/05/fig-4-olr-and-sst-0-10c2b0s2.jpg
Paul Vaughan (12:53:46) :
The wavelet approach gives monthly estimates of solar cycle length from monthly data …and without fussing around with “where was the max? where was the min?”
As solar cycles overlap by several years, the notion of THE minimum is physically dubious, no matter how the length is computed. You cannot invent physics with statistics.
tallbloke (14:35:47)
http://climatechange1.files.wordpress.com/2009/05/fig-4-olr-and-sst-0-10c2b0s2.jpg
–
Whoever produced that graph appears to have a handle on what the task is.
Where can I find the:
1) accompanying write-up?
2) OLR series? [& related references?]
I will again caution about ranges vs. means and local vs. global (since you list “global temperature”). I suspect it is going to take years before the research community’s momentum shifts far enough away from tradition & convention to embrace fruitful analyses that are not laden with spatiotemporal assumptions that dilute signals.
Anyone with mechanical insights is welcomed to comment on these observations, which relate to Agassiz, British Columbia, Canada (~49N, near sea-level, & near the west coast of North America – i.e. on the coastal side of the mountain range):
1) When Earth wobbles harder (6.4a timescale), extreme monthly maximum temperatures tend to be lowest (11a & 13a timescales).
2) When Earth wobbles harder (annual timescale), extreme monthly maximum temperatures tend to be lowest (4a timescale).
3) When Earth spins faster (annual timescale), minimum, extreme minimum, & mean monthly temperatures tend to be warmer (11a & 13a).
The most notable deviations from these (preliminary) generalizations occur in relatively recent years.
I am interested in broadening the investigation (spatially), but for now I just have results for the site I was paid to study for a year (which I at least know [first-hand] correlates strongly regionally (with some continental-coastal qualification)).
I hope to produce some presentable graphics when my schedule allows. There are so many ways to summarize this complex information visually — it is going to be a (minor) project just to figure out how to be most concise.
Leif Svalgaard (14:53:15) “As solar cycles overlap by several years, the notion of THE minimum is physically dubious, no matter how the length is computed.”
Agree.
Paul Vaughan (16:06:57) :
“THE minimum is physically dubious, no matter how the length is computed.”
Agree.
So, the quantity you are plotting has a dubious physical meaning, apt to confound any conclusions one might draw from relationships involving the cycle ‘length’ [the latter also being dubious].
Leif Svalgaard (14:53:15) “You cannot invent physics with statistics.”
One of the most brilliant statisticians I know once told me he prefers to avoid working on physics problems with physicists. I asked him, “Because of the ‘mechanism’ thing?” A grin slowly appeared on his face as he began nodding his head [yes]. It was a moment of shared humor. What to do when different disciplines, each with their own merit, see the world differently?…
I have noticed that a lot of statisticians like working with the medical/pharmaceutical community (since they get heralded as heros). Personally, that research has never interested me, even though the coin is better.
I investigate relationships, not causes. I qualify my statements about relationships; I do not claim causation. It is incumbent upon others (with the appropriate expertise) to sufficiently explain mechanisms; if/when that ever happens, climate research will no longer be needed.
This is a multi-disciplinary problem and it is crystal clear that many professing expert knowledge of the relevant physics need some lessons in statistics – and vice versa — but a human lifetime is not long enough to develop deep expertise across multiple fields, so one option appearing to have some practical merit (for society & individuals) is cooperation. If we all try to become experts in every field, the job might never get finished (for example, math is an endless world).
Cheers,
Paul.
Re: Leif Svalgaard (16:32:08)
You appear to misunderstand the method.
Paul Vaughan (19:27:53) :
Re: Leif Svalgaard (16:32:08)
You appear to misunderstand the method.
As usual, when there is misunderstanding, the onus is one the one who has something to communicate to clear it up.
The method is irrelevant if that which is supposed to be found with the method does not have much physical significance. And wavelet methods is part of any good physicists ‘cookbook’, e.g. http://www.leif.org/research/Asymmetric%20Rosenberg-Coleman%20Effect.pdf
Any statistical relationship or method is irrelevant if there is no underlying [real or a priori expected] physical relationship. ‘Hunting’ for relationships is not a valid enterprise: One looks at a hundred different things and expects by chance to find a handful, significant at the 95% level. So when you indeed find one, don’t declare it significant or undeniable.
Re: Leif Svalgaard (21:35:00)
Perhaps you misread “without” (as “with”). Otherwise: Do you seriously expect people to believe the series is stationary?
Leif Svalgaard (21:35:00) “‘Hunting’ for relationships is not a valid enterprise: One looks at a hundred different things and expects by chance to find a handful, significant at the 95% level. So when you indeed find one, don’t declare it significant or undeniable.”
This is pure distortion.
Paul Vaughan (15:01:15) :
tallbloke (14:35:47)
http://climatechange1.files.wordpress.com/2009/05/fig-4-olr-and-sst-0-10c2b0s2.jpg
–
Whoever produced that graph appears to have a handle on what the task is.
Where can I find the:
1) accompanying write-up?
2) OLR series? [& related references?]
It’s our old friend Erl Happ. Write up here; http://climatechange1.wordpress.com/2009/05/12/climate-change-a-la-naturale/
OLR for the tropics can be downloaded from;
http://www.cpc.noaa.gov/data/indices/olr
Paul Vaughan (01:26:51) :
Re: Leif Svalgaard (21:35:00)
Perhaps you misread “without” (as “with”). Otherwise: Do you seriously expect people to believe the series is stationary?
No, but the underlying phenomenon you are trying to depict is physically somewhat meaningless: the real length of a solar cycle is 13-18 years.
Paul Vaughan (01:30:33) :
Leif Svalgaard (21:35:00) “‘Hunting’ for relationships is not a valid enterprise: One looks at a hundred different things and expects by chance to find a handful, significant at the 95% level. So when you indeed find one, don’t declare it significant or undeniable.”
This is pure distortion.
But a fact, nevertheless. You say that you do not claim ‘causation’, but without such a claim, the exercise is meaningless.
Leif Svalgaard (05:03:54) “You say that you do not claim ‘causation’, but without such a claim, the exercise is meaningless.”
This statement is political.
Suggestion:
Spend a minute reproducing the transform I posted rather than wasting my time.
–
Leif Svalgaard (21:35:00) “One looks at a hundred different things […]”
This is where you went wrong – so your claim of “fact” is strawman-distortion.
When someone knows exactly what they are looking for and where to find it, there is just one efficient strike (no dice rolling).
–
Conceptual Understanding of Wavelet Analysis
Based on your comments, I question your conceptual understanding of the factors that can affect wavelet power. I encourage you to think very carefully about how the choice of wave & envelope affect local correlation in the time-timescale spectrum.
–
Terminology & Cross-Disciplinary Communication
As for your comment “the real length of a solar cycle is 13-18 years”, what is the temporal spacing between these? [no need to answer – rhetorical question – readers around here know the answer]
Perhaps you can deliver a brief lesson on comparative terminology in support of efficient cross-disciplinary communication. What do solar physicists want people to call the 11.1 year (on average) thing? (A precise technical term – on which there is broad consensus – would be most useful, if such a thing exists.)
I think you may find that this is a little like my beef with “running mean” vs. “moving average” – i.e. good luck shaking established conventions, whether ‘right’ or ‘wrong’. Other good examples of (misleading) terms we are stuck with (& tolerate): “imaginary numbers” & “standard error“.
I am (& others probably are) interested in knowing what the ‘preferred’ terminology is amongst solar scientists — and perhaps you can try to get a movement started to steer the general public’s use of terminology towards what you think it should be. [My choice is to not waste my energy leading a futile revolt against “imaginary”, “running”, & “error”.] Wouldn’t the simplest solution (considering reality & momentum) be to make use of 2 different adjectives in front of “solar cycle period” or “solar cycle length”? I await comment…
Paul Vaughan (14:01:59) :
When someone knows exactly what they are looking for and where to find it, there is just one efficient strike (no dice rolling).
If you claim no causation, then how does one know exactly what to look for and where to find it?
As for your comment “the real length of a solar cycle is 13-18 years”, what is the temporal spacing between these? [no need to answer – rhetorical question – readers around here know the answer]
There is no ‘temporal spacing’ that makes sense. The closest you can get to something that makes is to talk about the number of solar cycles per millennium, and from that compute a number. But it would be misleading to say anything about what the ‘length’ of a single cycle is.
What do solar physicists want people to call the 11.1 year (on average) thing?
We call it the ‘solar cycle’ [a misleading, but accepted term]. Everybody knows that it is not a real cycle and everybody knows that the cycle begins well before the ‘statistical’ minimum and extends well beyond the next minimum. Everybody knows that the minima are fiducial and not physical. Alternatively, one could count the cycle from polar field reversal to polar field reversal [roughly from ‘maximum’ to ‘maximum’]. This would be slightly better. There are some problems with that: 1) polar fields reverse at different times in each hemisphere, 2) may reverse multiple times within a short time [so how to define ‘the’ reversal], 3) assumes that polar fields always reverses in every cycle [so model dependent].
The best is not to attach any definite physical meaning to the minimum and to acknowledge that cycles overlap and that the average real ‘length’ of a ‘cycle’ is considerably longer than M, where M is the number you get by dividing a long time interval, T [say a thousand years – enough that end effects are small enough], by the number of cycles in T. Since we all know this, no [or little confusion] arises from this sloppy usage. Like we talk about electron ‘orbital’ well knowing the electrons are not like little planets ‘orbiting’ the nucleus; no confusion arises from this.
More on the ‘extended cycle’:
http://www.nature.com/nature/journal/v333/n6175/abs/333748a0.html
There is some debate if the extended cycle should be counted from the first to the last sunspot, or [the longer] time from first ‘sign’ of the new cycle [e.g. in the corona] to the last. The bottom line is that the precise time [even as determined by wavelet analysis or any other method] between successive minima [however defined] has little physical meaning. and that therefore, any relationship or conclusion that attaches meaning to that number is on shaky and dubious ground.
I don’t see any reason to ‘educate’ the public beyond the above and to try to establish a terminology. Since it is a sloppy thing to begin with, nothing is gained by trying to be semantically over-precise; on the contrary, it may confer a sharpness to the phenomenon that is not there to begin with.
Cameron and Schuessler http://arxiv.org/PS_cache/arxiv/pdf/0806/0806.2833v1.pdf discuss some of the pitfalls that follow by ignoring the overlap between cycles.
Paul Vaughan (14:01:59) :
“You say that you do not claim ‘causation’, but without such a claim, the exercise is meaningless.”
This statement is political.
You may have a political agenda, I don’t,
Suggestion: Spend a minute reproducing the transform I posted rather than wasting my time.
I assume that your computer can add and subtract and think that you have already wasted your time computing the time variation of a near meaningless number.
To simplify the analysis by Schuessler and Cameron and making it more accessible, let’s construct a simple example: A low cycle followed by a high cycle. The ‘official’ minimum [and I bet your wavelet minimum too] would be skewed towards the low cycle, making it shorter than it should be and the high cycle longer. A similar thing happens at the other end. So the length of the ‘cycle would be ‘convolved’ with the height of the surrounding cycles and would be a strangely weighted function of three cycles. This holds no matter how you define the minimum.
The way most solar physicists deal with this is to downplay [or simply disregard] papers or theories that take their starting point in the ‘length of a solar cycle’.
P.S. may I ask why your plot of ‘cycle lengths’omits that first and last ~50 years of the sunspot record? Avoidance of end-effects doesn’t seem to dictate such an excessive ‘overhang’.
Leif Svalgaard (17:14:20) :
To simplify the analysis by Schuessler and Cameron and making it more accessible, let’s construct a simple example: A low cycle followed by a high cycle. The ‘official’ minimum [and I bet your wavelet minimum too] would be skewed towards the low cycle, making it shorter than it should be and the high cycle longer.
If the cycles are asymmetrical, this effect can actually be reversed [what C&S really is after]. The important issue is that skewing occurs, depending on the sizes and asymmetries of adjacent cycles.
Leif Svalgaard (16:44:01) “I don’t see any reason to ‘educate’ the public beyond the above and to try to establish a terminology. Since it is a sloppy thing to begin with, nothing is gained by trying to be semantically over-precise; on the contrary, it may confer a sharpness to the phenomenon that is not there to begin with.”
We agree ^here.
–
Leif Svalgaard (16:44:01) “The bottom line is that the precise time [even as determined by wavelet analysis or any other method] between successive minima [however defined] has little physical meaning. and that therefore, any relationship or conclusion that attaches meaning to that number is on shaky and dubious ground.”
Key phrase: “[…] between successive minima [however defined] […]”
Now it is 100% clear that you misread (or misunderstood) my use of “without“. A wavelet transform treats all time series points as equals.
If you reread my initial comment in response to tallbloke, you will see that I was actually taking a swipe at methods that try to define a minimum (or maximum) and then try to base ‘cycle lengths’ (not ‘extended’ ones) on that. (I’ve gone through that exercise myself – it is messy & subjective – and it produces unsatisfying results.)
–
Leif Svalgaard (16:44:01) “If you claim no causation, then how does one know exactly what to look for and where to find it?”
It’s just Acoustics 101. As indicated a number of times, we need to work on rhythm. There is sufficient focus on amplitudes, but insufficient focus on phase relations (& their impact on linear correlation). Someone working on mechanisms will not know what the task is if there is no (undistorted) empirical picture available. Paradox will not seem illogical once we master the complexity. This will be achieved via deepening awareness of conditioning.
As an anecdote:
When I first learned wavelet analysis, I used to throw it at every possible combo (generating matrices). I quickly learned that while that might generate a lot of pretty pictures, it is (largely) a waste of time (& hard-drive space) (aside from the entertainment value).
Now I only bother to produce wavelet images when I know intuitively (from conceptual understanding) that they will provide a concise summary of something I already see. I work out all of the acoustics in my head while walking on the mountain – like I said: just Acoustics 101.
Don’t underestimate the flexibility & utility of wavelet methods Leif.
–
When you have some time, try this:
1) Generate a sine wave – call it A.
2) Do a Complex Morlet transform of A at a variety of wavenumbers.
3) Take the derivative of A – call the result B.
4) Repeat step 2 – but for B.
5) Compare the phase & power across A, B, & wavenumber.
6) Look at the cross-spectra for A & B (for varying wavenumber).
7) Repeat the preceding for sine-squared, higher-powered, & other-shaped waves (including absolute values).
8) Repeat with other wavelets.
9) Repeat with time-normalization of power.
10) Explore graphical portrayal of resonance by studying phase differences for harmonics.
–
Thanks for the solar physics insider-notes – appreciated as always.
Leif Svalgaard (17:14:20) “[…] [and I bet your wavelet minimum too] […] no matter how you define the minimum.”
You need to review my other comments to overcome your misunderstanding/misreading. Again: There is no definition of a minimum in the wavelet analysis.
–
Leif Svalgaard (17:14:20) “[…] may I ask why your plot of ‘cycle lengths’omits that first and last ~50 years of the sunspot record? Avoidance of end-effects doesn’t seem to dictate such an excessive ‘overhang’.”
As explained previously (in a recent thread), Morlet 2pi is a bandwidth hog. This is the cost of frequency resolution – it is a tradeoff – basic Wavelet 101.
Elaboration:
I do not pad with zeros (or assume cyclicity or do anything else) to create “fantasy extensions” off the edges. In this case you can see that I also snipped off the edge-contamination related to the time-normalization – which is over a narrowing timescale-band towards the ends (a more serious problem at the 1800 end due to the high power at 13a) (not a problem at the 1960 end until the cone-of-influence intersects the ~10.5a power-band). I have no use for the “edge fantasies” that pollute publications – & btw editors should consider cracking down on this misleading [but seemingly conventionally accepted] [mal]practice.
A useful webpage – addressing time- vs. timescale- resolution tradeoffs:
http://www.clecom.co.uk/science/autosignal/help/Continuous_Wavelet_Transfor.htm
This becomes interesting when one starts investigating resonance using wavelet methods. For example, if there is loose resonance, a Complex Mexican Hat cross-wavelet transform will show higher frequency phase-difference variations than the corresponding cross-wavelet transform for Complex Morlet 2pi. Such comparisons provide a means of assessing robustness of findings. NO POLITICS HERE – JUST CAREFUL INVESTIGATION.
Paul Vaughan (18:14:33) :
Don’t underestimate the flexibility & utility of wavelet methods
I don’t. Use them myself, but [as it seems you do too], only as tools to confirm and quantify what I already see or know. As I said, you can’t invent physics with statistics.
When I first learned wavelet analysis, I used to throw it at every possible combo (generating matrices)
This is what I meant when I said that if one tries a hundred things, one should be surprised if a handful show significance at the 95% level.
But back to the science, since the cycle length is ill-defined [and depends on the shape of neighboring cycles], what is the purpose of doing the analysis in the first place?
Paul Vaughan (19:07:13) :
You need to review my other comments to overcome your misunderstanding/misreading. Again: There is no definition of a minimum in the wavelet analysis.
No, it is up to you to [as I always do in great detail] to elucidate [repeat ad nauseam, if necessary] the process. There may not be an explicit definition, but an implicit one, because the power depends on the values. Try this experiment: make 15 cycles [identical in amplitude and period – e.g. triangular]; then make the middle cycle twice as high, plot the resulting wavelet power.
–
“may I ask why your plot of ‘cycle lengths’omits that first and last ~50 years of the sunspot record?”
I do not pad with zeros (or assume cyclicity or do anything else) to create “fantasy extensions” off the edges.
So, you could not do the analysis if you only had 100 years of data?
Paul Vaughan (19:07:13) :
There is no definition of a minimum in the wavelet analysis.
Since it goes after the amplitude of the sunspot number, the analysis may be meaningful as an indication of the ‘recurrence’ period of solar activity, that is, the time from one maximum to the next. Since this is not what [some] people ordinarily call the solar cycle length, there is amble room for confusion here [since extended cycles overlap]. Better would be some notion of repeat time of activity ‘pulses’ [subject to some stochastic variations], instead of the fixation on the [misleading] ‘solar cycle length’.
Leif Svalgaard (19:24:27) :
Paul Vaughan (18:14:33) :
“When I first learned wavelet analysis, I used to throw it at every possible combo (generating matrices)”
This is what I meant when I said that if one tries a hundred things, one should be surprised if a handful show significance at the 95% level.
One should NOT be surprised …, of course.
Leif Svalgaard (19:32:45) “So, you could not do the analysis if you only had 100 years of data?”
You could – but you would have to use a different wavelet — for example: Morlet with a lower wavenumber. This would inevitably lead to tradeoffs. When I’ve tried this tactic for some time series, I have ended up tossing out the results (because sometimes they simply do not stand up to scrutiny).
However, I don’t think it is preferable to invent “fantasy extensions” (which is common & misleading [mal]practice).
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Leif Svalgaard (19:24:27) “This is what I meant when I said that if one tries a hundred things, one should be surprised if a handful show significance at the 95% level.”
I knew very well & exactly what you meant. I’ve taught & judged 1000s of statistics students …and my point [as I think you see now, based on your other comments] is that I’m not running “crap-shoot” “shot-in-the-dark” analyses — these comments:
Leif: “[…] [as it seems you do too], only as tools to confirm and quantify what I already see or know.”
Re: Leif Svalgaard (20:10:59)
You appear awfully eager to quote that OUT-OF-CONTEXT.