An apology to Dennis

[Roger Chapman]

I doubt that there was any real truth in most of what you wrote.

How would you summarise your conclusions?

Let me do it for you.

That the max/min average is is yet another unknown variable with no relationship to the true mean. Not even as an approximation.

That the 9am temperature is to be preferred as it is at a precise time while the maximum and minimum temperatures are worthless as the timing is varied.

That 24 hours is an arbitrary period for which an average temperature is of no relevance.

That you would use as your primary time period for determining a yearly average a lunar month of 27.8 days or perhaps a decade.

The average of -14 and 5 is -9.

Every one of these statements is based on what you have said and they all have something else in common. They are all garbage.

When I have put forward real figures to illustrate my points you have either alleged I have been fiddling the figures or you have ignored them.

As I have said before lack of imagination is another of your many faults.

[Tim Streater]

Righto.

[Tim Streater]

How are you defining (and measuring) the true mean?

[Roger Chapman]

So you didn't read the DIY data thread either. :-)

The software on my computer has a current month summary page and the true mean figures just above are culled straight from that.

I have the recording rate set at every 15 minutes but the weather station transmits its information every few seconds and most probably the data logger averages each 15 minute period before giving up the information. However the destructions are a bit hazy and I haven't checked back to make sure this particular set-up is that competent. Even if it is only the 15 minute average that would be the true mean for all practical purposes.

Where I have quoted true means for January I have had to copy and paste the data into a spreadsheet to average all 96 entries for a day which would be more than a bit time consuming for a month.

[Roger Chapman]

snip

Have you considered the possibility that all 3 daily temperatures are taken from the same thermometer and are thus subject to the same hazards that you have postulated for the maximum and minimum readings?

[Clot]

I shall be rude: Pillock.

[Clot]

Dad, are we there yet?

[dennis]

clot.

[Roger Chapman]

snip

I don't think you have ever said why you think that averaging the daily

9am temperatures will give a close approximation of the annual average temperature. You have so far ignored my suggestion that the relationship between each day's 9am temperature and the average temperature for the day is, to say the least, uncertain so what is your justification.

Have you perhaps concluded that the uncertainty in the 9am temperatures with respect to the daily average is sufficient to make them a truly random selection so that their average would automatically provide the annual average within the usual caviat of sampling error?

[Grimly Curmudgeon]

We were somewhere around Barstow, on the edge of the desert, when the drugs began to take hold. I remember "The Medway Handyman" saying something like:

Pennsylvania six five oh oh oh.

[ARWadsworth]

Playground chant. As in Fight, Fight, Fight......

Adam

[Man at B&Q]

Pedantically, what you are calculating is the median temp.

That's why it's an approximation. For many days, without wild swings in temp between the min and max, it will be a fairly close approximation.

MBQ

[dennis]

I don't recall anyone other than you suggesting it would. It will give you the average 9 am temp which is just as likely to prove GW as the true average temp or the average min or the average max.

We don't care, that isn't what has been said.

[Roger Chapman]

Did you not notice this?

"Note that these are the 9am temperatures, which I believe is a more reliable measurement than the average of the maximum and minimum daily temperature."

Or are you still plugging the nonsense that the average of max and min doesn't give an average at all.

And then of course there is the bit from Matty F above in which he claims that the 9am temperatures have not risen for a long period while the max/min averages have. They should show the same trends, albeit with more variability in the case of the 9am temperature, which is the reverse of what he is claiming.

Now did you omit the max/min average because you don't consider it an average at all or because it will make your statement above even more false than it is now? The true mean will have tighter confidence limits than the max/min average but the max/min average will have tighter confidence limits than the 9am average. (ie the max/min average will be more reliable than the 9am average). You cannot read anything directly into separate averages for maximum and minimum. To get the average temperature for the year you need to average the two which will gicve the same result as averaging the daily averages.

The questions were posed for Matty F. Are you now his official spokesman? If so perhaps you would like to answer the question below in the continued absence of Matty from the discussion.

[dennis]

Where does it say it is a better average? Why do you insist on comparing them to the average which is not available either by measurement or by calculation. What exactly are you trying to prove?

He says they declined not that they should have done anything. Its the climatologists that say things are rising.

I omit it because it has an unknown error built in. You don't appear to be able to understand this and are going to repeat the same cr@p arguments again.

It can't be more reliable than an actual measurement, it is a calculated guess, nothing more.

No it does not. It tells you if the actual measured temps have changed not the ones you have guessed at.

Its irrelevant, you are the only one talking about average daily temps from random times.

[Roger Chapman]

snip

Where does what say which particular element is a better average, and better than what? If you mean of max and min are you at last conceding that that is an average.

There you go again pretending that the average of maximum and minimum doesn't bear any relationship to the true mean.

That should be obvious but one unintended result is that I have proved you know next to nothing about statistics, not to mention to your hilarious failure to average -14 and 5 correctly.

He said that the temperatures are declining [marginally] but the climatologists using data from the same location say the temperatures are rising significantly. We both assumed that the professionals would have used a max/min average but given that the data all came from the same location both averages should exhibit the same trends. It is just that the confidence limits for the 9am data would be much wider.

There you go again. No understanding of numbers whatsoever.

I am sure that the 9am temperature would be as precise as the maximum and minimum temperatures. But what use is that when it fluctuates much more that the max/min average.

Yes it does.

((a1 + b1)/2 + (a2 + b2)/2 + ...(an + bn)/2)/n =((a1 + a2 + ...an)/n + (b1 + b2 + ...bn)n)/2

It is still the mid point that is significant.

No, that is just your take on the subject. The timing of maximum and minimum is uncertain but it certainly isn't random, so we will have to add random to the list of words you use but don't understand.

[dennis]

What are you on? Its pointless talking to you so you can join TMH.

[Roger Chapman]

More evidence of your lack of imagination in mirroring one of my previous comments. What you write is frequently ambiguous and you often take advantage of that ambiguity to retrospectively change what you apparently intended to say. "Where does it say it is a better average" is really just another in a long line of non sequiturs from you where the lack of connection with what it is supposedly commenting on leaves the options wide open.

So at long last you have finally realised that when you are in a hole the most prudent course of action is to stop digging. You may now have time to practice averaging two numbers, one of which is a negative.

[dennis]

You are being more stupid by the second. There is no where anyone has said the 9 am temp is an average, you are the one that insists on creating a mathematical average for two data points an what is effectively a chaotic system and claiming it is better than an actual physical measurement at a known time. It isn't, it can't be and never will be.

At least I can understand a simple concept of what is real data and what is made up unlike you. Lets see what the possible errors are..

Time.. 9 am +- a few seconds, temp x +- error in instrument

vs.

Time unknown so 12:00 +- 12, temp somewhere between min and max, so temp = average +- max-min/2

and you still insist that its a better "measurement".

Bye!

[Roger Chapman]

I know it is not the done thing to reply to one's own posts but now that Dennis has retired hurt there are a couple of points I still wish to clarify.

The message itself been savagely snipped but anyone who wants a good laugh at Dennis's expense should go back and and compare the original to see the points Dennis silently snipped to avoid answering.

snip

So what do we know about the average of maximum and minimum temperatures for a 24 hour period?

Well the first and most obvious point is that it is an approximation of the true mean (by which I mean the average of the continuous temperature curve).

There will be (in most instances at least) some difference between the average and the true mean but this offset will never be as extreme as to equal either limit and in practice will usually be close to the true mean.

Measure this offset over the course of a year and the mean and standard deviation can be calculated. Continue to measure over a number of years and the mean and standard deviation of the year by year variation of the offset can be calculated and one would then be in a position to work out the confidence limits of the average temperature for any year for which the max/min temperatures are known.

This of course is the long winded way of doing it to prove even to innumerate idiots like Dennis that while the max/min average for an individual 24 hour period may not be precisely the same as the true mean the long term average of the max/min temperature has a relationship to the true mean that can be defined within narrow limits.

snip

The actual pattern of temperature change during any 24 hour period can be very varied and it does happen that the warmest point may be just after dawn or the coldest in the middle of the afternoon which is the reverse of the steady state pattern in which the atmosphere starts cooling soon after the sun reaches its zenith and continues to cool until the sun is in a position to start warming the atmosphere again. If the timing of maximum and minimum was indeed random then the long term average temperature for the 12 hours from 6am to 6pm would be the same as that for the 12 hours from 6pm to 6am.