thaumaturgy
Well-Known Member
Any one who believes one can get a 1 degree signal out of a 4 deg SD is also making a freshman level error. And that is what you are doing.
Let me introduce (again) the confidence interval.
The Confidence Interval based on the z-statistic (for large sample sizes normally distributed) has the following form:
95% CI = 1.96* s/sqrt(N)
s = standard deviation
N = number of data points
(Confidence Intervals)
Would you like an example?
Here's one:
If I have 1000 samples and the standard deviation of the mean of the data is 1 and the standard deviation is 4 the 95% confidence interval is:
1+ 1.96* (4/10) = 1+ 0.8
That means that with repeated sampling there is a 95% chance that the true mean will be within plus or minus 0.8 units.
NOTE: The confidence interval is only 20% the size of one standard deviation.
I know I've gone over this before.
Indeed if we have a heavy tailed distribution the standard deviation is a bit over estimated than if it were a nice gaussian distribution, but indeed the 95% confidence interval can be smaller than a standard deviation.
I have been and I clearly disagree. With a narrow distribution with heavy tails it pretty much means that while there may be large outliers there are still a huge amount of signal within a reasonable limit of error.I am not saying it is signal. I am saying it is mostly noise--haven't you been paying attention?
With sufficient data you can even estimate the true mean rather narrower using the confidence interval.
This is pretty much intro stats.
Are you serious on this point? Honestly? These are two themometers located 20 miles apart read by some guy (or guys) who drive out to the site every day at about the same time, but they are just instruments and they are just humans, and you expect that the temperature, let's say on a day when the average is 50degF to differ by no more than 4% relative error?If we are really measuring temperature correctly we shouldn't have many 2 degree differences in temperaure.
And you won't allow that there might be, on occasion, actual differences in temperature?
But further you keep studiously avoiding the really important fact that the trends are what is most important in this discussion.
Even if one thermometer read 5 degrees above the other consistently as long as they both moved in the same direction and with the same relative magnitude the trend is still preserved.
That is why one usually resorts to measuring the trend rather than the absolute.
This is also why, in chemistry, it is often easier to measure the change in energy in a system than the "absolute energy" of the system.
If you look at every single blip of noise in any data set and you try to assign a real physical effect you are interpretting noise as signal.No, you have been too busy ignoring physics.
Let me ask you, when you flip around on the AM radio dial do you stop on the static stations and try to figure out if it's really Rush Limbaugh talking to you? Or do you keep scanning until you find a real signal? Because right now it sounds like you might sit and listen to the static trying to figure out if this is just a new form of language.
No, quite the contrary. The key point was to show that there was a lot of points above and a lot below and they seemed relatively randomly distributed. Not like for one whole year the whole data set was above zero and one year below zero. I will grant there does seem to be a consistent offset in the 365 point running median of about 0.2 degrees F.Then it was in appropriate of you to claim that you couldn't see the offset.
No, I was making a point. If one cannot make a point here without being accused of "propoganda" or lying I am unsure how to procede.In the chart you post now, you can learly see the bias in the data, and it varies over time. For years at a time it is biased one direction and then for years at a time it is biased another. By your clipping the axes, you were engaging in propaganda, not scientific analysis.
No, I would expect them to average to about the same temperature. There is noise in every system.Man, you really don't listen at all do you. Let's start with simple physics. If you set two thermometers on a golf course far from a building, you would expect them to read the same temperature.
Let's put it this way: if my technician came to me with a pile of data that was supposedly repeated measurements and they all agreed perfectly, I'd ask them to do it over again because that doesn't look real to me.
Maybe that just comes form about 30 years in the experimental sciences, I don't know.
So why do you think these have outliers? Have you ever made a mistake in measuring something? Ever written a number down wrong? How about times when you didn't realize you'd made a mistake?If, over time, they varied wildly, you would think something is wrong. Same thing with cities 20 miles apart. I dont' expect them to vary much more than a degree on the daily mean, yet regularly they vary by 4-5 degrees.
Sorry, just accusing me of ignorance is not an effective strategy. Especially when I'm the one who understands the difference between a confidence interval and a standard deviation.That is why the difference is important. We can't check up on the temperature reading in a single city series, but we can compare it to a town that should have the same temperature. This little fact has gone over your head in both of our debates.
Hmm.Yes I am accusing you of that, and maybe worse. You are the one who clipped the axes cutting off any chance to see the bias in the data and then you pounded your chest and acted as if it was idiotic to think that there was a bias. That shows either incompetence or worse.
No, the median difference over about a century is less than 1 degree. But that seems to be escaping you.If they were all within a degree, I would have no case to make. But as can be seen, they most assuredly are not within a degree. They aren't even within 2 degrees often.
I am so far the only one dealing with statistics at more than the high school level.You continue to claim that the thermometer data is good in spite of bad gauges. Is it because you BELIEVE and your science be damned?
I cannot stress this enough. The point of clipping the axes was to show that the data was distributed around zero.If you really believed that the gauges were bad, you wouldn't keep trying to make them OK as you are doing.
Are there air conditioners at one of the two Mississippi stations? Please show me the information. Were they there in 1915?the land data is crap. I will say it again. You can only assess the same trend if the airconditioner isn't running on either station.
And I would dearly hope you don't! I wouldn't want anyone to believe what I say just because I say it. That is why I obsessively (and I do mean obsessively) provide links to my sources, and the calculations and links to information behind the formulae I use.Honestly you can run what you want, but I am not likely to trust what you say.
You are thus not required to believe a single word I say.
As you wish.You are the guy who clipped the axes and who depended upon a borehole study which dumped 95% of the data in order to achieve a result. You hadn't done enough research to even know that the previous borehole study existed. And if you had, then you failed to mention a very important piece of contradictory data--that too is anti-science.
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