@okie,
Quote:My guess is that it may not be worth sampling the temperature curve more than we do now, but obviously more data points provide a more accurate average, that was the debate here I thought. And if one station is off by maybe a half degree, how can multiplying that by all the stations cure the inaccuracy.
I thought you understood statistics.
The error in measuring may be in one direction but the error in trend can not be. Global warming only looks at the trend.
Let's assume all the measurement stations are off by some degree. Now we use the data from them over a period of time. Unless the error specifically trends one way, the error itself won't matter because the average over time will correct that error.
Look at it this way okie. Roll a pair of dice and record the number. Now do this 10 times. Add the numbers together and divide by the total number of chances. In 10 chances, the odds are good that the average will be about 7 and most likely between 6 and 8. Now roll the dice 100 times. The odds are even better that the average will be 7. The more times you roll the dice the more likely it is that the average from all the rolls will be 7. Eventually there comes a point that no matter how many more times you roll the dice you won't get closer to or farther from 7 because the sheer amount of data reduces the effect rolling a 2 or a 12 will have on the overall data. If you were to graph all your rolls, you would see that there is no trend in the data.
But let's introduce an error into the dice. Let's add 6 to the total. That means if you roll a 2 you record it as 8. If you roll a 12 you record it as 18. Roll the dice 100 times and graph the trend. Even though the dice totals are always wrong compared to what the dice actually were you still get the same trend line as if you didn't add 6.
Now if you want to, you can introduce a random error to your dice. Roll 2 dice then roll a third die and add the number from that die. Roll them enough times and you will see that the trend is the same as just rolling 2 dice.
Now.. get 30 pairs of dice.
Roll each pair 30 times and record their average. They won't all be exactly the same with only 30 rolls but if you were to add them together you have 90 rolls so the likelihood of it equaling 7 would be pretty good.
Now using the average you just produced for each pair of dice continue to roll each pair another 10 times. Now graph each pair against the the average. Some will show a trend going higher than the average, some will show it going lower but if you add them all up, the odds are pretty good they will show little to no trend.
Now get 500 pairs of dice (weather stations). Roll them 100 times (100 years of data for one day). Now, repeat rolling 100 times 365 more times (for each day of the year) for a total of 36,500 rolls for each pair of dice. For each 100 times you roll the dice use 30 consecutive rolls to figure what the average roll should be. Now instead of recording the number from the rolls, only record how far it is from the average. It doesn't matter how many spots on the dice or even if you use different numbers of spots for each pair, (A winter day would be -20 to 5 and a summer day would be 10-45) the likelihood of seeing a trend from random numbers goes down. You will only see a trend if you change the dice in a given pair.
