# More Proof That Global Warming Is Toast **URL:** \ **Category:** Great Debates\ **Created:** [October 20, 2008, 3:23pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742 "2008-10-20T15:23:40Z")\ **Posts on this page:** 20\ **Page:** 9
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [November 24, 2008, 9:44am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/161 "2008-11-24T09:44:14Z")
> [@mbedell](#): > > In fact, scientists are now saying that we entered a period of global cooling. What percent of them? And _scientists_ of what specialty? There’s an amazing number of lawyers and software engineers who are considered climate scientists by the blogosphere. ---
**Author:** ![mbedell](https://avatars.discourse-cdn.com/v4/letter/m/edb3f5/32.png) [@mbedell](https://boards.straightdope.com/u/mbedell)\ **Post date:** [November 25, 2008, 8:17pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/162 "2008-11-25T20:17:49Z")
_What percent of them? And scientists of what specialty? There’s an amazing number of lawyers and software engineers who are considered climate scientists by the blogosphere_ SageRat, I dont know. I just dont have the time to do the research for you. However, I am being truthful when I say that I have seen several articles on Internet news websites that discuss scientists findings. ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [November 26, 2008, 8:09am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/163 "2008-11-26T08:09:13Z")
> [@brazil84](#): > > You are making a rookie mistake here, which is to assume that temperature measurements for each give time period are independent – like firing a new round at a target. You misunderstand deeply and with great fervor. The point behind comparing a known distribution (measured temperatures) to a random normal distribution (see post #153) and finding a low probability is to show that the **known distribution is unlikely to be the product of random activity**. If you had read my post more carefully, you might have noticed: > [@wevets](#): > > My natural response is to say we’re **not looking at a data set normally distributed around 0.1444°C** – we’re looking at a data set with an upward trend. (bolding added, but still mine) I’m telling you that we’re not looking at a randomly distributed data set and you’re trying to argue with me by saying that the measurements aren’t independent and therefore aren’t randomly distributed! If it’s a “rookie mistake” (your words) then why do you **agree** with it??? 😕 Why would you call something a rookie mistake and then in the very next dependent clause endorse it yourself? If I didn’t know better I’d think you took my joke about Bayesians vs. Frequentists too seriously. > [@brazil84](#): > > Going back to your Texan analogy, suppose that the Texan fires a group of 10 shots. One can compute a sample mean and sample standard deviation for the group of shots. If an 11th shot then falls 1 standard deviation from the mean, can one conclude that he must have been shooting at a different target? Of course not. Again, you missed a salient point I made in an earlier post: > [@wevets](#): > > In 1988, what happened was different from what happened in 1983. In 1988, the 5 year running mean of global temperature anomalies went outside the standard deviation of global temperature anomalies for the past century by 0.016°C\*\*. Now recall that means are measures of center. Individual years would have a 16% probability of appearing more than one standard deviation above the 1980 value, but the 5 year running mean is different because it is a measure of center. > … > Think back to our shooting Texan. He’s fired off a sequence of rounds, changed magazines, and fired off a second set. In this analogy, each individual year is like an individual bullet. Each magazine of bullets is like the 5-year running mean. I keep bolding the words **measure of center** in the hope that you will eventually notice that they are different from “data point.” 😉 > [@brazil84](#): > > I believe that there is no need to curtail CO2 emissions because their likely effect on the climate will not be significantly negative. Clear enough? Yes – but the more interesting question is **why** you believe that. Even if, as you say, Richard Lindzen is 100% correct, you still need to curtail CO[sub]2[/sub] emissions because you’ll eventually triple CO[sub]2[/sub] in addition to doubling it. You just get more time in which to complete the move away from fossil fuels. > [@brazil84](#): > > I’m a little confused – are you saying that even if Richard Lindzen is 100% correct and Hanson is wrong, we still need to curtail CO2 emissions? Just to be thorough, the answer is yes. Note that Lindzen’s estimates are just at the lowest end of this range: [Stabilization scenario graph.](http://en.wikipedia.org/wiki/Image:IPCC_AR4_WGIII_GHG_concentration_stabilization_levels.png) > [@brazil84](#): > > This makes no sense at all. Natural temperature trends can and do occur. For example, the Little Ice Age. I never said natural temperature trends didn’t occur. I think you need to re-read this part of my post: > [@wevets](#): > > Temperatures are increasing. **You may not have noticed that I haven’t yet addressed at all why** – the Texan could be changing targets or he could have chugged a six-pack of PBR between magazines, but there’s little point in discussing that unless we at least agree that the GW is happening. Once we agree on GW, only then does it make sense to talk about AGW (which I haven’t talked about yet) or “CAGW.” I haven’t yet in this thread discussed why I believe the current temperature trend is not just natural, but has a significant man-made component too. You were arguing against statements I hadn’t made yet! Here, let me make your job easier by actually saying something about that. **Why I think the warming has a significant man-made component.** [ul]Measurement of other potential warming factors produces no inputs sufficient to account for the observed warming. Here’s a [graph](”[File:Radiative-forcings.svg - Wikipedia](http://en.wikipedia.org/wiki/Image:Radiative-forcings.svg) “) of the relative strengths of various forcings. Also see Table 6.11 on [this page](”[http://www.grida.no/publications/other/ipcc\_tar/?src=/climate/ipcc\_tar/wg1/212.htm](http://www.grida.no/publications/other/ipcc%5Ftar/?src=/climate/ipcc_tar/wg1/212.htm) “).[/ul] [ul]Modeling known inputs of both anthropogenic and natural forcings allows accurate hindcasting of the observed temperature trend, while modeling known inputs of only natural forcings does not. [An example](http://www.grida.no/publications/other/ipcc%5Ftar/?src=/climate/ipcc_tar/wg1/index.htm) of the difference between models with and without anthropogenic forcings. If you don’t like the models aspect, then just think about the forcing calculations (see [this page](”[http://www.grida.no/publications/other/ipcc\_tar/?src=/climate/ipcc\_tar/wg1/222.htm](http://www.grida.no/publications/other/ipcc%5Ftar/?src=/climate/ipcc_tar/wg1/222.htm) “)) independent of the GCMs.[/ul] [ul]Rate of warming appears to be inconsistent with past warming events that had natural causes. [For example](”[File:Holocene Temperature Variations.png - Wikipedia](http://en.wikipedia.org/wiki/Image:Holocene_Temperature_Variations.png) “), it took about 500 years for the temperature anomaly to rise 1ºC at the end of the last glaciation 10,000 years ago. We’re up about 0.9ºC since the 1700s (300 year spans being the shortest we can estimate rates in the proxy records, or if you want to compare apples and oranges, 0.9ºC in the last 150 years using thermometer records.[/ul] I’m sure you disagree with one or more of these, so let’s discuss whichever one appeals to you. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [November 26, 2008, 8:14am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/164 "2008-11-26T08:14:54Z")
Oh, the _Internet_! Why didn’t you say so? That makes it all OK.\* Of course\* you don’t have to cite, then, that’s alright. ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [November 26, 2008, 11:09am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/165 "2008-11-26T11:09:52Z")
> [@wevets](#): > > You misunderstand deeply and with great fervor. The point behind comparing a known distribution (measured temperatures) to a random normal distribution (see post #153) and finding a low probability is to show that the **known distribution is unlikely to be the product of random activity**. If you had read my post more carefully, you might have noticed: No, you are the one who has a deep misunderstanding. Your mistake is to assume that natural processes will produce random distributions of temperatures. Nothing could be further from the truth. (ETA: Assuming I understand your position correctly. See below.) A hypothetical, followed by a couple questions, will demonstrate it: Suppose you are a group of medieval monks in Europe who make accurate temperature measurements from 1400 to 1600; figure out an average temperature for each year; and then subject the distribution of temperatures to a statistical analysis. (1) Do you agree that by traditional statistical analysis, the temperatures will show a statistically significant decline over that time period? (2) Do you agree that the mean of the later years (1500-1600) will be significiantly outside the variation from the earlier years (1400-1500)? (3) If so, what (if anything) can our group of monks infer from these observations? > [@](#): > > I’m telling you that we’re not looking at a randomly distributed data set and you’re trying to argue with me by saying that the measurements aren’t independent and therefore aren’t randomly distributed! I’m telling you that there is no reason to expect the measurements to be randomly distributed. Again, look at my hypothetical. > [@](#): > > If it’s a “rookie mistake” (your words) then why do you **agree** with it??? 😕 Why would you call something a rookie mistake and then in the very next dependent clause endorse it yourself? You misunderstood my point, which is unsurprising given that you haven’t corrected your mistake yet. Try answering my hypothetical questions above. > [@](#): > > In this analogy, each individual year is like an individual bullet. Each magazine of bullets is like the 5-year running mean. I keep bolding the words **measure of center** in the hope that you will eventually notice that they are different from “data point.” 😉 You are the master of your own analogy, so let me recast my point: Suppose that an additional magazine of 10 rounds is fired and the mean location of the new rounds is such that it’s a one-sigma event. Assuming that the variation takes place in only one dimension, that might mean that the mean location is approximately 3/10 sample standard deviations away from the mean location of the first group of shots. Ok, now can we conclude that the shooter changed his target? Of course not. My point stands. Because any way you slice it, a one sigma event is a one sigma event. > [@](#): > > Yes – but the more interesting question is **why** you believe that. Even if, as you say, Richard Lindzen is 100% correct, you still need to curtail CO[sub]2[/sub] emissions because you’ll eventually triple CO[sub]2[/sub] in addition to doubling it. You just get more time in which to complete the move away from fossil fuels. Do you understand that, as far as anyone knows, each additional increase in CO2 will have less of an impact on the climate? Do you understand that some time in the next 1000 years or so, the earth will almost certainly enter a serious ice age (absent intervention)? > [@](#): > > I never said natural temperature trends didn’t occur. I think you need to re-read this part of my post: I haven’t yet in this thread discussed why I believe the current temperature trend is not just natural, but has a significant man-made component too. You were arguing against statements I hadn’t made yet! Here, let me make your job easier by actually saying something about that. 😕 Earlier, you said this: > [@](#): > > warming of the last century or so is not small compared to natural variations on the same timescale. Were you claiming that recent temperature increases are not within the range of natural variation? Or that they are? ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [November 26, 2008, 3:17pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/166 "2008-11-26T15:17:34Z")
Just to follow up on my previous post, I think it may be helpful to quote an exchange from the previous page: **Me:** And how would you refer to the position of people like me, which is that mankind’s CO2 emissions are likely result in warming, but such warming will be small compared to normal variations in temperature and in any event will not cause significant negative consequences? **Wevets** : I think the boat has already sailed on recent warming being small compared to natural variations in temperature. We’ve known for decades that the warming of the last century or so is not small compared to natural variations on the same timescale. So you seemed to be arguing that warming over the last century is sufficiently out-of-the-ordinary that one can conclude it’s attributable to man-made causes. In any event, I would ask that you clarify your position on this point. ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [December 5, 2008, 6:15am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/167 "2008-12-05T06:15:43Z")
> [@brazil84](#): > > No, you are the one who has a deep misunderstanding. Your mistake is to assume that natural processes will produce random distributions of temperatures. Nothing could be further from the truth. (ETA: Assuming I understand your position correctly. See below.) You do not understand my position correctly, as I have pointed out before and will do again here. I make no assumption that natural processes produce random temperatures. Where are you getting that from? The most likely explanation is that you may be confusing the assumption that **variation around the mean at one specific time is random** (which I have made\*) with an assumption that natural processes produce random distributions of temperature (which I have not made.) There is an important, and rather large, difference between those two assumptions. There may be a less likely explanation for your thinking I’ve made an assumption that I haven’t. Feel free to elaborate if that is the case. Here is what I am doing. 1. The assertion is that current temperatures are not indicative of an unusual rising trend (see your post # 144) 2. We can ask: Are the temperatures of the late 1980s and early 1990s really any different from those of the late 1970s and early 1980s? (time periods chosen by a Hansen paper published in 1981 referenced above.) 3. We compare those temperature distributions and see if they are statistically indistinguishable. In this case, they turn out to be very easily distinguishable from each other. 4. It doesn’t make sense to criticize this comparison on the basis of an assumption that “natural processes produce random distribution of temperature” (your words.) The reason it doesn’t make sense is that the answer to question #2 above could be that the temperatures of those two time periods are the same – i.e. that all the differences can be attributed to random variation. You are accusing me of making an assumption that was one of the potential outcomes, and the one that the math didn’t support (see post # 153.) If you’re going to make an accusation that I’ve made an assumption instead of performing a test, **it would make more sense to accuse me of assuming the answer I got instead of accusing me of assuming the answer I didn’t get!** 😛 > [@brazil84](#): > > I’m telling you that there is no reason to expect the measurements to be randomly distributed. And I’m telling you that **we can demonstrate that** the measurements are not randomly distributed. Why is this a disagreement? Perhaps it will help you if I explain in the terms of your hypothetical: > [@brazil84](#): > > Suppose you are a group of medieval monks in Europe Well, in that case I set fire to Brother Maynard for believing in the heresy of Monophysitism. 😃 > [@brazil84](#): > > who make accurate temperature measurements from 1400 to 1600; figure out an average temperature for each year; and then subject the distribution of temperatures to a statistical analysis. > > (1) Do you agree that by traditional statistical analysis, the temperatures will show a statistically significant decline over that time period? > > (2) Do you agree that the mean of the later years (1500-1600) will be significiantly outside the variation from the earlier years (1400-1500)? > > (3) If so, what (if anything) can our group of monks infer from these observations? What you seem to be building up to is: (4) But the climate change from 1400 to 1600 was natural! Sorry (well, not really sorry – it’s just an expression) if I stole your thunder. 🙂 The problem is again that you haven’t been reading my posts very carefully. Demonstrating that 1988 is significantly different from 1981 does not demonstrate that the difference is man-made, and I have never said that it does. > [@wevets](#): > > You may not have noticed that I haven’t yet addressed at all why – the Texan could be changing targets or he could have chugged a six-pack of PBR between magazines, but there’s little point in discussing that unless we at least agree that the GW is happening. Once we agree on GW, only then does it make sense to talk about AGW (which I haven’t talked about yet) or “CAGW.” From post #153. This is the third time I’ve posted that statement – perhaps third time’s the charm? In this analogy, the Texan changing targets could be anthropogenic climate change, while the Texan chugging a six-pack of PBR could be natural climate change. > [@wevets](#): > > If I see that the measure of center of our Texan’s new group of bullets is further away than the measure of spread from the center of his old group of bullets, I’m going to be very suspicious that he’s shooting at his new face (or possibly that he’s drunk – we can’t discount that at this point.) Oops. I actually said it twice in post #153, and two more times after that, and again quoted directly above. Five times and counting. So let’s get back to this: > [@brazil84](#): > > (3) If so, what (if anything) can our group of monks infer from these observations? What the results indicate is that significant changes in temperature are occurring, and that these changes are occurring rapidly. We can rule out potential factors that would change the temperature very slowly (such as orbital precession.) We can list the few things that could change the atmosphere’s global average temperature rapidly – _Solar irradiance_ – Solar irradiance has not increased enough to account for the observed temperature changes. > [@Foukal et al.](#): > > Variations in the Sun’s total energy output (luminosity) are caused by changing dark (sunspot) and bright structures on the solar disk during the 11-year sunspot cycle. The variations measured from spacecraft since 1978 are too small to have contributed appreciably to accelerated global warming over the past 30 years. > > … > > Overall, we can find no evidence for solar luminosity variations of sufficient amplitude to drive significant climate variations on centennial, millennial, and even million-year timescales. From: Foukal et al. 2006. Variations in solar luminosity and their effect on the Earth’s climate. _Nature_ v. 443, pgs. 161-166. _Volcanism_ – Sufficient volcanism to account for global warming remains unobserved. > [@USGS](#): > > Our studies show that globally, volcanoes on land and under the sea release a total of about 200 million tonnes of CO2 annually. > This seems like a huge amount of CO2, but a visit to the U.S. Department of Energy’s Carbon Dioxide Information Analysis Center (CDIAC) website ([http://cdiac.ornl.gov/](http://cdiac.ornl.gov/)) helps anyone armed with a handheld calculator and a high school chemistry text put the volcanic CO2 tally into perspective. Because while 200 million tonnes of CO2 is large, the global fossil fuel CO2 emissions for 2003 tipped the scales at 26.8 billion tonnes. Thus, not only does volcanic CO2 not dwarf that of human activity, it actually comprises less than 1 percent of that value. From: [Hawaiian Volcano Observatory](http://hvo.wr.usgs.gov/volcanowatch/2007/07_02_15.html) _Asteroid/Cometary Impact_ - The observed increases in temperature rule this out (asteroid and cometary impacts should cause a dramatic decrease) even if we could somehow be struck by an object and not have people notice. _Human action_ – It just happens that industrial societies pour vast amounts of exactly the same type of gases that retain more heat than the pre-industrial atmosphere could, and in the [right amount](http://en.wikipedia.org/wiki/Image:Radiative-forcings.svg) to account for observed warming. _Inhuman action_ – If all hell breaks loose, undoubtedly temperatures will rise, since [Hell is exothermic](http://www.pinetree.net/humor/thermodynamics.html). Cats and dogs living together and mass hysteria have not yet struck, so all Hell has not broken loose. Just some Hell as in many places [men can marry men](http://www.nytimes.com/2008/10/11/nyregion/11marriage.html?hp). And that’s not even Hell breaking loose in a bad way, either. 😉 > [@brazil84](#): > > Do you understand that, as far as anyone knows, each additional increase in CO2 will have less of an impact on the climate? If you follow [this link](” [http://en.wikipedia.org/wiki/Image:IPCC\_AR4\_WGIII\_GHG\_concentration\_stabilization\_levels.png”](http://en.wikipedia.org/wiki/Image:IPCC_AR4_WGIII_GHG_concentration_stabilization_levels.png%E2%80%9D)), you’ll note that we do know the shape of the curve by which additional units of CO[sub]2[/sub] influence eventual temperature stabilization. Note that all the curves in that graph are the same shape, including the upper and lower bounds. Despite uncertainty regarding the exact values of temperature given a [CO[sub]2[/sub]], the shape does not change. This is a mistake I see a lot – the existence of _any_ uncertainty is mistaken for _complete_ uncertainty. > [@brazil84](#): > > Do you understand that some time in the next 1000 years or so, the earth will almost certainly enter a serious ice age (absent intervention)? Isn’t it ironic? Don’t you think? A little too ironic; yeah I really do think. It’s like coming from a person who doesn’t thinks the uncertainties in a 100 year climate projection are too large, without realizing that the uncertainties in a 1000 year climate projection are even larger. (With apologies to Alanis Morisette, the word “irony” for its misuse, and Sesame Street sponsor the letter Q.) > [@brazil84](#): > > Suppose that an additional magazine of 10 rounds is fired and the mean location of the new rounds is such that it’s a one-sigma event. Assuming that the variation takes place in only one dimension, that might mean that the mean location is approximately 3/10 sample standard deviations away from the mean location of the first group of shots. What exactly is this supposed to mean? The only way I can parse it is inherently self-contradictory (it can’t be both 3/10ths of a standard deviation and 1 standard deviation away at the same time,) so perhaps you could rephrase? \*As it turns out, we can entirely do away with that assumption too and get the same result. Although the technique was not known in the 16th century, so our hypothetical monks wouldn’t know how to do this, you could do a Runs Test for Trend Data. The Runs Test for Trends Data is a quick-and-dirty way to assess for trends or randomness that doesn’t require data to meet the assumptions of other tests. Here’s how it works: Take our 5-year running means and characterize each as an increase or decrease from the previous mean. Year – 5 year running mean – increase or decrease? 1980 – 0.1444 – N/A 1981 – 0.1887 – Increase 1982 – 0.1765 – Decrease 1983 – 0.1513 – Decrease 1984 – 0.1354 - Decrease 1985 – 0.1701 – Increase 1986 – 0.1735 – Increase 1987 – 0.1993 – Increase 1988 – 0.2608 – Increase 1989 – 0.2957 – Increase 1990 – 0.2762 – Decrease 1991 – 0.2630 – Decrease 1992 – 0.2775 – Increase 1993 – 0.2832 – Increase 1994 – 0.2701 – Decrease 1995 – 0.3245 – Increase 1996 – 0.3952 – Increase 1997 – 0.4178 – Increase 1998 – 0.4108 – Decrease 1999 – 0.4578 – Increase 2000 – 0.4769 – Increase 2001 – 0.4730 – Decrease 2002 – 0.5007 – Increase 2003 – 0.5491 – Increase 2004 – 0.5594 – Increase 2005 – 0.5572 – Decrease 2006 – 0.4459 – Decrease 2007 – 0.3391 – Decrease If you count up the number of years that can be used then n=27 and r=12 (r is the number of runs – sets of like signs together surrounded by different signs.) t[sub]s[/sub] = (r – [(2n-1)/3])/{the square root of [(16n-29)/90]} t[sub]s[/sub] = (12-[(2_27-1)/3])/{the square root of [(16_27-29)/90]} = -2.6779 Since we have n\>25, we can compare this test statistic to a normal distribution (N.B.: I think this is the step that confused you earlier. Comparing a test statistic to a normal distribution is not the same as assuming a normal distribution is the appropriate representation of real-world data, in fact it is one of the steps in demonstrating that the normal distribution is not the appropriate representation.) The expected number of runs is about 17.67, and the 95% confidence interval is 13.52 to 21.81. 12 runs is significantly less than that with p=0.05, so we can conclude that the data show at least one systematic trend. Therefore, these temperatures do not represent random variation. If we couldn’t measure the output of the sun or volcanoes we could be forgiven for thinking they were the cause, but we can measure those things. ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [December 5, 2008, 6:18am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/168 "2008-12-05T06:18:10Z")
I should have mentioned - I’m sure you’ll respond fairly quickly, but I won’t be back until the end of December. Until then, Merry Christmas/Hanukkah/Winter Solstice/Consumerism Orgy! ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [December 5, 2008, 2:32pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/169 "2008-12-05T14:32:26Z")
> [@wevets](#): > > You do not understand my position correctly, as I have pointed out before and will do again here. I make no assumption that natural processes produce random temperatures. Where are you getting that from? From the exchange I quoted in post #166. > [@](#): > > 1. The assertion is that current temperatures are not indicative of an unusual rising trend (see your post # 144) > 2. We can ask: Are the temperatures of the late 1980s and early 1990s really any different from those of the late 1970s and early 1980s? (time periods chosen by a Hansen paper published in 1981 referenced above.) > 3. We compare those temperature distributions and see if they are statistically indistinguishable. In this case, they turn out to be very easily distinguishable from each other. Assuming that your statement in (3) is correct, it does not follow that my assertion in (1) is incorrect. This is because temperature trends can and do happen, which you seem to concede. In other words, your question is largely irrelevant to my claim. > [@](#): > > Perhaps it will help you if I explain in the terms of your hypothetical: > > What you seem to be building up to is: > (4) But the climate change from 1400 to 1600 was natural! > > Sorry (well, not really sorry – it’s just an expression) if I stole your thunder. 🙂 The problem is again that you haven’t been reading my posts very carefully. Demonstrating that 1988 is significantly different from 1981 does not demonstrate that the difference is man-made, and I have never said that it does. That’s what you seem to have implied when you stated that “We’ve known for decades that the warming of the last century or so is not small compared to **natural** variations on the same timescale.” (my bold) It seems to me that a medieval monk using your logic could have made the same statement as Europe entered the Little Ice Age. > [@](#): > > What the results indicate is that significant changes in temperature are occurring, and that these changes are occurring rapidly. I’ve stated both explicitly and implicitly throughout the thread that temperatures rose last century. So I’m not sure what your point is, except possibly to attack a strawman. > [@](#): > > We can list the few things that could change the atmosphere’s global average temperature rapidly In your view, what caused temperatures to increase so rapidly in roughly the first half of the 20th century? > [@](#): > > If you follow [this link](” [http://en.wikipedia.org/wiki/Image:IPCC\_AR4\_WGIII\_GHG\_concentration\_stabilization\_levels.png”](http://en.wikipedia.org/wiki/Image:IPCC_AR4_WGIII_GHG_concentration_stabilization_levels.png%E2%80%9D)), you’ll note that we do know the shape of the curve by which additional units of CO[sub]2[/sub] influence eventual temperature stabilization. Note that all the curves in that graph are the same shape, including the upper and lower bounds. Despite uncertainty regarding the exact values of temperature given a [CO[sub]2[/sub]], the shape does not change. Lol. I guess that means “yes.” > [@](#): > > It’s like coming from a person who doesn’t thinks the uncertainties in a 100 year climate projection are too large, without realizing that the uncertainties in a 1000 year climate projection are even larger. (With apologies to Alanis Morisette, the word “irony” for its misuse, and Sesame Street sponsor the letter Q.) :shrug: Some processes are much easier to predict than others. With respect to ice ages, there’s no need for a supercomputer to know that one likely coming (absent non-natural intervention) All you need is your eyeballs and a little common sense. [http://www.seed.slb.com/en/scictr/watch/climate\_change/images/global\_temp2.jpg](http://www.seed.slb.com/en/scictr/watch/climate_change/images/global_temp2.jpg) > [@](#): > > What exactly is this supposed to mean? The only way I can parse it is inherently self-contradictory (it can’t be both 3/10ths of a standard deviation and 1 standard deviation away at the same time,) so perhaps you could rephrase? Apparently you have never taken probability and statistics. I don’t really have time to teach it to you (and I’m a bit rusty myself), but basically the standard deviation of the arithmetic mean of n normal variables, each from the same distribution with standard deviation sigma will be the square root of n times sigma. In this case, the square root of 10 is approximately 3. We can make it 3.16 if you like. Feel free to correct me if you know better, but if you don’t know better, please don’t pretend. > [@](#): > > Therefore, these temperatures do not represent random variation. So what? We already agree that “natural” does not necessarily mean “random.” As I asked you before, what in your opinion caused the rapid increase in temperatures in roughly the first half of the 20th century? ---
**Author:** ![Sailboat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sailboat/32/461_2.png) [@Sailboat](https://boards.straightdope.com/u/Sailboat)\ **Post date:** [December 5, 2008, 4:51pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/170 "2008-12-05T16:51:17Z")
> [@mbedell](#): > > It was a scam from the start. Whenever there is money involved someone, like Gore, will try and exploite it. Scientists can be bought off to give their “expert” opinion. This thinking baffles me. The amount of money hypothetically being made from “promoting” AGW cannot, I am sure you must agree, _cannot begin_ to approach the amount of money tied up in current oil and energy and industrial practices. If AGW is real enough to requuire change, it will impact almost everything we do that makes money. So you could create a chart: AGW “promotion” “profits” vs. “All the money in the world now invested in status-quo processes that would have to change if AGW is real.” It’s absolutely clear that the second category contains untold trillions of dollars – probably more dollar value than all the money circulating on earth, since it represents hundreds of years of investment in some cases. Your saying that money wins, right? People can be bought? Yet you argue that your hypothetical moneymaking fledgling AGW promotion industry not only attracts more scientists and more dollars than “all the money in the world now invested in status-quo processes”? And further, you’re arguing that the other side – the one with the vast bulk of the world’s money, and fear of change – is NOT buying scientists and spending money to influence the outcome? Oil companies are somehow saints but scientists are corrupt? It’s patently absurd once you follow the logic through. If moneyed interests are influencing the AGW debate, you can be _absolutely certain_ that the advantage is hugely on the side of the deniers (your side). Since you perceive that the AGW discussion is robust and not going your way, you are drawn – if you are following the logic – inescapably to one of two conclusions: 1. Money is _not_ (sufficiently) impacting the AGW debate. In other words, you are wrong in your assertion. 2. The evidence for AGW is so strong that, _despite the influence of money_, which you now can see runs heavily against belief in AGW, this evidence is winning hearts and minds. The truth is coming out anyway. Which is it? Sailboat ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [December 5, 2008, 6:43pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/171 "2008-12-05T18:43:26Z")
> [@Sailboat](#): > > This thinking baffles me. The amount of money hypothetically being made from “promoting” AGW cannot, I am sure you must agree, _cannot begin_ to approach the amount of money tied up in current oil and energy and industrial practices. It seems to me that there is an assumption in your argument that the financial interests of folks like Hansen and Gore necessarily conflict with the financial interests of the Oil Industry. Although it may seem like that on the surface, I’m not sure it’s really the case. Consider the current situation: Folks like Gore and Hansen are getting a lot of money/funding and attention. At the same time, the oil industry is pumping, refining and distributing like usual. For Gore to make a lot of money, he doesn’t actually have to succeed in getting the world to drastically reduce its carbon emissions. Indeed, the world is cranking out more carbon than ever and shows few signs of letting up. So the oil industry is making money; Gore is making money; Hansen is getting funded; the IPCC delegates are getting attention, funding, travel, etc. Everyone wins, right? Well not exactly. As usual, the taxpayers are bled a little bit. Also envirnonmental causes which aren’t as sexy as global warming are losing a bit. ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [January 6, 2009, 2:43am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/172 "2009-01-06T02:43:28Z")
I see now that you’re confusing the concepts of **comparing** and **combining**. > [@brazil84](#): > > Apparently you have never taken probability and statistics. I don’t really have time to teach it to you (and I’m a bit rusty myself), but basically the standard deviation of the arithmetic mean of n normal variables, each **from the same distribution with standard deviation sigma** will be the square root of n times sigma. You see, here you have **combined** the two groups of shot the Texan fired (recall post #[163](http://boards.straightdope.com/sdmb/showpost.php?p=10498132&postcount=163)) that I am **comparing**. Your mistake is in the assumption that these sequences of shots are from the same distribution. That is the question we are trying to answer: are they from the same distribution? Any introductory textbook in statistics will tell you that the standard deviation is calculated as the square root of (the sum of squares divided by your sample size minus one.) More simply put, it is the square root of the variance. s = √{(∑y[sup]2[/sup])/(n-1)} where ∑y[sup]2[/sup] = ∑ (Y-Y[sub]bar[/sub]) You’ll see this formula using slightly different symbology on the [wikipedia page for standard deviation](http://en.wikipedia.org/wiki/Standard_deviation#Estimating_population_standard_deviation_from_sample_standard_deviation). The formula you want to use is, instead, the formula for the standard deviation of **combined** samples, as you can see here on the [wikipedia page](http://en.wikipedia.org/wiki/Standard_deviation#Relationship_between_standard_deviation_and_mean). Unfortunately for you, we do not know if it is appropriate to combine samples – we are trying to figure out if the two sequences of shots the Texan fired are part of the same distribution (in other words, was he firing both sequences of shots at the same target and in the same state of sobriety?) You would probably benefit from reading a simple explanation of the process of calculating standard deviations: Here is the appropriate method for comparing two groups which you don’t know if they come from the same distribution (i.e. apples and oranges.) [Here is the appropriate method](http://www.stats4students.com/Essentials/Sampling/Overview_4.php) for combining two samples from the **same population** and calculating the standard deviation of means. > [@brazil84](#): > > Feel free to correct me if you know better, but if you don’t know better, please don’t pretend. Thank you, I have written the correction above. ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [January 6, 2009, 11:24am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/173 "2009-01-06T11:24:21Z")
> [@wevets](#): > > I see now that you’re confusing the concepts of **comparing** and **combining**. > > You see, here you have **combined** the two groups of shot the Texan fired (recall post #[163](http://boards.straightdope.com/sdmb/showpost.php?p=10498132&postcount=163)) that I am **comparing**. No, I’m “comparing” (to use your words). Here’s what I said before: > [@](#): > > Suppose that an additional magazine of 10 rounds is fired and the mean location of the new rounds is such that it’s a one-sigma event. Assuming that the variation takes place in only one dimension, that might mean that the mean location is approximately 3/10 sample standard deviations away from the mean location of the first group of shots. See? In my hypothetical one calculates the mean of each group of 10 shots and the sample standard deviation of the first group of 10 shots. Then one looks at the mean of the second group and sees that it’s approximately 3/10 of a standard deviation away from the (sample) mean of the first group. That’s a one-sigma event, which you would know if you remembered your first year statistics. Let’s do it this way: 1. You look at the first group of 10 shots and calculate a sample mean and sample standard deviation. 2. You look at the second group of 10 shots and calculate a sample mean. 3. You observe that the sample mean of the second group is approximately 3/10 of a standard deviation away from the sample mean of the first. 4. Do you agree that this (roughly speaking) is a one-sigma event? > [@](#): > > Any introductory textbook in statistics will tell you that the standard deviation is calculated as the square root of (the sum of squares divided by your sample size minus one.) More simply put, it is the square root of the variance. I asked you not to pretend that you know what you are talking about if you don’t. Yes that’s true, but it does not contradict my hypothetical or undermine it in any way. Here’s the question you asked, which I have answered: > [@](#): > > it can’t be both 3/10ths of a standard deviation and 1 standard deviation away at the same time, * * * Anyway, you have unfortunately ignored the most important question in my last post, which I asked twice. I will ask it again: What in your opinion caused the rapid increase in temperatures in roughly the first half of the 20th century? ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [January 6, 2009, 11:34am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/174 "2009-01-06T11:34:23Z")
> [@brazil84](#): > > No, I’m “comparing” (to use your words). To add to my last post, what I am “combining” (again to use your words) are the 10 shots in each group. Ironically, I am doing this “combining” at your insistence, because earlier you said this: > [@](#): > > In this analogy, each individual year is like an individual bullet. Each magazine of bullets is like the 5-year running mean. I keep bolding the words measure of center in the hope that you will eventually notice that they are different from “data point.” Now that I have done essentially what you asked, you claim that there is something wrong with it. Lol. But anyway, please don’t ignore the question I’ve been asking again and again: What in your opinion caused the rapid increase in temperatures in roughly the first half of the 20th century? ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [January 11, 2009, 5:11am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/175 "2009-01-11T05:11:32Z")
I’ve been trying to stick to the same analogy in the hope that it will make it easier to understand. Let’s take it from the beginning – recall that the purpose of the analogy is to help you to understand the concept of a five year running mean. Our Texan lines up with the barn and fires off a set of five rounds (the number is five because the analogy is to help explain a **five** year running mean. You changed it to ten in post #[155](http://boards.straightdope.com/sdmb/showpost.php?p=10451126&postcount=155155).) Let’s imagine the barn is a coordinate system starting with (0,0) at the lower left hand corner of the barn. Bullets from Magazine A: 3.06708, 1.13396 2.99700, 1.20240 2.95975, 1.18159 2.94949, 1.13181 3.17726, 1.38711 The center of this grouping (mean in x and y) is (3, 1.2). The standard deviation of distances from this point is 0.13. Note that the deviations from the mean are almost exactly the same size as the deviations from the 5-year temperature anomaly mean of 1980. Funny coincidence (by which I mean deliberately engineered to be so,) isn’t it? The Texan pauses to change magazines in his rifle. Now he fires 5 more bullets, hitting: Bullets from Magazine B: 3.21658, 1.15173 3.10493, 1.22355 3.09875, 1.22173 3.14091, 1.15401 3.20076, 1.26928 The center of this grouping is (3.15, 1.2). The standard deviation of the distances from this point is 0.08. Note that the deviations from the mean are almost exactly the same size as the deviations from the 5-year temperature anomaly mean of 1988. The concern is not that a bullet from magazine B is more than one standard deviation away, but that the center of all magazine B’s bullets is more than a standard deviation away from magazine A’s center. Also, the center of magazine C’s bullets (1996’s five year mean) is two standard deviations away from magazine A’s center, and the center of magazine D’s bullets (1999’s five year mean) is three standard deviations away from magazine A’s center, and the center of magazine E’s bullets (2004’s five year mean) is four standard deviations away from magazine A’s center. A blind emu could see this trend, and an [Electric Monk](http://www.cs.bham.ac.uk/~ard/adams.html) would only need the processing power of a 1950 wristwatch to believe in the trend. So let’s see how you propose to examine this trend: > [@brazil84](#): > > Let’s do it this way: > > 1. You look at the first group of 10 shots and calculate a sample mean and sample standard deviation. > > 2. You look at the second group of 10 shots and calculate a sample mean. > > 3. You observe that the sample mean of the second group is approximately 3/10 of a standard deviation away from the sample mean of the first. > > 4. Do you agree that this (roughly speaking) is a one-sigma event? This still doesn’t work, although it’s an improvement that you have switched to the sample standard deviation instead of the standard deviation of means for your first step. If you really must use a standard deviation of means, there is a way to do it - let me correct it for you (the parts different from your suggestion are bolded): 1. Look at the first group of shots and calculate a sample mean and sample standard deviation. **2. Look at the second group of shots and calculate a sample mean and sample standard deviation.** **3. Treat both groups of shots as samples of the same population, and calculate a mean of means and a standard deviation of means.** (I obviously don’t prefer this method because it requires additional time and calculations, but it would be wrong of me to say you can’t use inference here instead of deduction.) 1. Observe how close the sample means are **to the population mean** using the standard deviation of means as a metric. One of your problems is here: > [@brazil84](#): > > 1. You observe that the sample mean of the second group is approximately 3/10 of a standard deviation away from the sample mean of the first. > > 2. Do you agree that this (roughly speaking) is a one-sigma event? By step #4, the only standard deviation you have calculated is the standard deviation of the first group of shots. Therefore, your standard deviation of the means is: σ[sub]means[/sub] = σ[sub]First Group[/sub]/√1 = σ[sub]First Group[/sub] Since you only have 1 sample and its sample standard deviation to calculate your standard deviation of means. You need to calculate the standard deviations of at least two samples to get a different answer. You see, as I said above, calculating a σ[sub]means[/sub] requires **combining** multiple samples. Look, I recommend that you do this with a separate window or tab open to [http://www.stats4students.com](http://www.stats4students.com) or a statistics book open next to you – it’s the internet - no one’s going to know! Just like no one here knows I have Sokal & Rohlf’s _Biometry_ sitting next to my laptop as I type this. 😉 There’s another mistake in there too: > [@brazil84](#): > > 1. Do you agree that this (roughly speaking) is a one-sigma event? No. “Events” are not means/averages. “Events” are something that happens, and the only thing that actually happens in statistics is the measurement that produces a data point. The only thing in statistics that is an “event” is a data point – everything else is a calculation that comes out the same regardless of when the calculation is made. Your desire to conflate means/averages and data points is obvious in this post: > [@brazil84](#): > > Going back to your Texan analogy, suppose that the Texan fires a group of 10 shots. One can compute a sample mean and sample standard deviation for the group of shots. If an 11th shot then falls 1 standard deviation from the mean, can one conclude that he must have been shooting at a different target? Of course not. It’s understandable that ideology demands that you treat a mean as the same as a data point, but no one is fooled. But I’m curious: what demands that you resort to _ad hominems_ like this: > [@brazil84](#): > > Lol. Despite that you hypocritically ban _ad hominem_ in your own “rules of debate.” ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [January 11, 2009, 11:25am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/176 "2009-01-11T11:25:47Z")
> [@wevets](#): > > I’ve been trying to stick to the same analogy in the hope that it will make it easier to understand. No, you’ve changed the analogy again to make things more complicated. Earlier, the only question was whether the shooter had changed targets so one could reasonably assume that the standard deviation of the distribution for the second group of shots was the same as that of the first. Now you’ve thrown that assumption out the window. It looks to me like the only reason you are doing so is that you can find fault with my analysis. > [@](#): > > The concern is not that a bullet from magazine B is more than one standard deviation away, but that the center of all magazine B’s bullets is more than a standard deviation away from magazine A’s center. And one can calculate just how unusual of an event that is. Assuming normal distributions, the standard deviation of the mean of 5 shots will be roughly 0.44 times the standard deviation for the distribution. So you would be looking at (roughly) a 2 sigma event. Ok, so how does that feed back in to your original claim? I’ll quote your source just to refresh your recollection: * * * > [@](#): > > When should the CO2 warming rise out of the noise level of natural climate variability? An estimate can be obtained by comparing the predicted warming to the standard deviation, σ, of the observed global temperature trend of the past century (50). The standard deviation, which increases from 0.1°C for 10-year intervals to 0.2°C for the full century, is the total variability of global temperature; it thus includes variations due to any known radiative forcing, other variations of the true global temperature due to unidentified causes, and noise due to imperfect measurement of the global temperature. **Thus if T0 is the current 5-year smoothed global temperature, the _5-year smoothed global temperature_ in 10 years should be in the range T0 ± 0.1°C with probability ~ 70 percent, judging only from variability in the past century.** The predicted CO2 warming rises out of the 1σ noise level in the 1980’s (my emphasis) See? Your **own source** computes the 1 sigma threshhold in terms of where the 5 year moving average goes. Assuming that everything your source says is correct, what supposedly happened in the 1980s is merely a 1 sigma event. > [@](#): > > No. “Events” are not means/averages. “Events” are something that happens, and the only thing that actually happens in statistics is the measurement that produces a data point. The only thing in statistics that is an “event” is a data point – everything else is a calculation that comes out the same regardless of when the calculation is made. The fact is that your **own source** made the claim that the 5 year average of temperatures crossed the one sigma threshhold in the 1980s. Your source, not mine. If it makes you uncomfortable to call that an “event,” call it whatever you want. It makes no difference to the analysis. > [@](#): > > It’s understandable that ideology demands that you treat a mean as the same as a data point, but no one is fooled. Lol. That’s the most ridiculous thing you’ve said in this entire thread. YOUR SOURCE combined data like this. I am combining data like this because you have insisted on doing so in your analogy. ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [January 11, 2009, 11:35am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/177 "2009-01-11T11:35:10Z")
> [@wevets](#): > > But I’m curious: what demands that you resort to _ad hominems_ like this: > Despite that you hypocritically ban _ad hominem_ in your own “rules of debate.” It’s not an ad hominem. Just because your argument is laughably silly doesn’t make you a bad person. Anyway, speaking of debating rules, Rule 3 provides that you must answer reasonable questions to help me understand your position. Again and again, I have asked you the following question: \*\*What in your opinion caused the rapid increase in temperatures in roughly the first half of the 20th century? \*\* And again and again you have ignored it. It’s a reasonable question and I would like an answer to help me understand the basis of your claim regarding the entire temperature rise over (roughly) the last century. So kindly answer my question. (Note that my answer would be “I don’t know.”) \*\*What in your opinion caused the rapid increase in temperatures in roughly the first half of the 20th century? \*\* Your choice. ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [January 16, 2009, 4:23am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/178 "2009-01-16T04:23:38Z")
> [@brazil84](#): > > Assuming normal distributions, the standard deviation of the mean of 5 shots will be roughly 0.44 times the standard deviation for the distribution. So you would be looking at (roughly) a 2 sigma event. So are you trying to say that Hansen (and I, since I agree with his cite here) are underestimating how easily the trend could be detected by a factor of two? ---
**Author:** ![brazil84](https://avatars.discourse-cdn.com/v4/letter/b/8491ac/32.png) [@brazil84](https://boards.straightdope.com/u/brazil84)\ **Post date:** [January 16, 2009, 4:37pm UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/179 "2009-01-16T16:37:17Z")
> [@wevets](#): > > So are you trying to say that Hansen (and I, since I agree with his cite here) are underestimating how easily the trend could be detected by a factor of two? No. I am trying to say that a one sigma event is a one sigma event. Assuming that Hansen’s statistical analysis is correct, the fact that the 5 year moving temperature average crossed the one-sigma threshhold is not strong evidence of anything. It’s not strong evidence of a statistically significant positive trend in temperature, and it’s certainly not evidence of variation which is not natural. (The first issue is of course academic, since in 2009, few dispute that there has been a significant postive trend in temperature over the relevant time period.) In any event, you have chosen to ignore my simple, reasonable question yet again. (Instead, you have spent many pages trying to weasel out your earlier statement.) Bye. ---
**Author:** ![wevets](https://avatars.discourse-cdn.com/v4/letter/w/e9a140/32.png) [@wevets](https://boards.straightdope.com/u/wevets)\ **Post date:** [January 21, 2009, 4:37am UTC](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742/180 "2009-01-21T04:37:00Z")
> [@brazil84](#): > > No. I am trying to say that a one sigma event is a one sigma event. You’ve chosen a spectacularly poor way of phrasing that then: > [@brazil84](#): > > Suppose that an additional magazine of 10 rounds is fired and the mean location of the new rounds is such that it’s a one-sigma event. Assuming that the variation takes place in only one dimension, that might mean that the mean location is approximately 3/10 sample standard deviations away from the mean location of the first group of shots. > [@brazil84](#): > > Assuming normal distributions, the standard deviation of the mean of 5 shots will be roughly 0.44 times the standard deviation for the distribution. So you would be looking at (roughly) a 2 sigma event. I’m not too sure of the best way to argue “A is A,” but I am confident that stating “A is 0.44xA” is not high on the list. Especially when it’s quite clear that you’re conflating σ[sub]means[/sub] with σ[sub]sample[/sub]. From: [http://www.stats4students.com/Essentials/Sampling/Overview\_4.php](http://www.stats4students.com/Essentials/Sampling/Overview_4.php) > [@](#): > > For example, if there were 100,000 students aged 16 in the population, then this gives us 1,000 samples of size 100 (100,000 ÷ 100 = 1,000). > … > From this mean value (that is, the mean of the sample means) and distribution (that is the distribution of sample means), we can calculate the standard deviation of the distribution of sample means, which is called the standard error of the mean, . This is simply the standard distance that a sample mean is from the population mean. This standard distance (or error) is calculated by taking the population standard deviation, σ, and dividing it by the square root, , of the sample size, n. You’re trying to compare your σ[sub]means[/sub] with your **sample** mean, and you’re not even calculating a population mean. The best part is - it doesn’t even give you the answer you want! 😛 You’re trying to say the trend was undetectable in 1988, and to do that you want the new mean to be fewer standard deviations away, not more! 😃 > [@brazil84](#): > > Assuming that Hansen’s statistical analysis is correct, the fact that the 5 year moving temperature average crossed the one-sigma threshhold is not strong evidence of anything. As Hansen states, it is evidence of a trend. Interestingly, a trend you admit exists. So you want to admit the trend exists, but pretend Hansen didn’t detect it 20 years ago, despite the fact that he’s on public record talking about it back in the '80s. Not a hill I would choose to die on, but hey, whatever floats your boat. > [@brazil84](#): > > It’s not strong evidence of a statistically significant positive trend in temperature, and it’s certainly not evidence of variation which is not natural. Strawman. One I addressed back in post [#167](http://boards.straightdope.com/sdmb/showpost.php?p=10533573&postcount=167). > [@brazil84](#): > > In any event, you have chosen to ignore my simple, reasonable question yet again. Don’t you have a “rule of debate” against switching subjects? > [@brazil84](#): > > It’s not an ad hominem. Just because your argument is laughably silly doesn’t make you a bad person. Are you unfamiliar with the definition of [_Ad hominem_](http://en.wikipedia.org/wiki/Ad_hominem)? It’s attacking the source and not the substance, which is what your favorite acronym does. There is no requirement that the target be a bad person. You can direct _ad hominem_ against MLK, Gandhi, or Albert Schweitzer. [Other posters](http://boards.straightdope.com/sdmb/showpost.php?p=10601526&postcount=326) have noted your predilection for an acronym that doesn’t reflect your state of mind. Since we all know you’re not actually laughing, there’s an excellent chance your overuse of LOL is instead intended to convince yourself. Which is actually rather sad. ☹ [Previous page](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742.md?page=8) [Next page](https://boards.straightdope.com/t/more-proof-that-global-warming-is-toast/468742.md?page=10)