Ned - I moved this response up from a question you asked in a prior thread.
Of course each presidential term is not the same. So what?
It's not that these terms differ. It's that they are not independent samples from the same, identical distribution. All these these statistical tests are based on this assumption.
People are taught statistical formulas without being taught the conditions under which each formula is valid. For better or for worse, these statistical formulas are very widely used when the proper circumstances do not exist. Even professional researchers all too often ignore this requirement. As a result, they get wrong results. This is a big issue today in the statistical community. Look up John Ioannidis for more info.
The next judgment is this: given that one's data doesn't match the [implicitly] assumed conditions, how close is it? IMHO, this variable -- Stock Market growth during a Presidential Term -- is not close at all to independent, identically distributed data. Therefore, there's no validity to measuring Dem vs Rep using these statistical formulas.
DiC: That's all just assertions. You simply declare that the data are not iid and imply that the departure from iid is severe enough to matter. But you don't show it.
I could come up with some rationales/arguments for why they might not be iid. Is the departure large enough to matter? Shrug.
David Appell: Thanks for the new chart. Note that the WHO data for Italy seem to be the same as the Worldometers data but lagged by 1 day, and the WHO data for the USA seem to be a rough approximation of the Worldometers data for the USA but lagged by *2* days.
So the WHO data seems to show Italy 11 days ahead of the USA, while the Worldometers data shows Italy ahead by 10 days.
Here is another version of your chart, based on the Worldometers data, and with the cases log-transformed:
It's scary how closely the USA is following Italy. Note also the blue dashed line, which is the trend for the USA data. A linear trend in the log-transformed data would be constant exponential growth. So far it's quite linear, but over the next 10 days Italy's rate seems to be slowing down a bit (dropping below the trend line). Is that due to the adoption of control measures? Or inadequate testing once the numbers get too big? Or that testing was lagging behind and caught up, after which the growth rate appeared to slow? Or the virus starting to reach some natural limit to its growth?
I am curious whether the USA will stay on that line, or start to drop below it like Italy. Increased testing in the USA could lead to an apparent increase in the rate. Widespread adoption of social distancing could slow it.
Of course on a per-capita basis, the case counts in the USA are 5x lower than what this indicates. They're still growing at the exponential rate, but it would be longer before we have the same density of cases. It looks like on a per-capita basis, the USA is 16-17 days behind Italy, depending on whether you use the Worldometers or WHO data.
With an inept and ineffective federal government, through 51 states to 300 million individualists, you seem to be finding it difficult to decide on a common policy and a coordinated response.
The US trend has been very closely following an exponential growth function, which appears linear on the natural log version above. Extrapolating that to late March would give approx 1230 cases per million, or 400,000 cases total, in the USA.
However, Italy's rate of increase seems to be slowing. If the US follows the same path, it would be more like 100,000 cases nationwide.
I hope our newfound interest in social-distancing helps, and we bend the curve downward to stay below 100,000 cases in March.
USA has tested about 20,000 on march 15th, and is now testing a few thousand a day.
Canada has tested about 23,000, and is now testing a few thousand a day, but we are hitting some issues ramping up to the levels needed. I expect USA will surpass us in a day or so.
My mom has been sick with a cough for weeks. They haven't tested her, but don't believe she has it. She's pretty vulnerable right now either way.
Schools and libraries are closed. Businesses are going online only. We'll know in two weeks whether this is enough to stem the tide.
PS: Per capita, Canadian case numbers are running at 73% of the US's.
But that was this morning. At 1 pm there were about 950 new cases in the US compared the same time yesterday, a one-day increase of about 40%. Deaths were up about 15%.
Today's press conference with Trump and Pence and the health experts was encouraging. Starting tomorrow, the number of tests will be going up like a rocket. BTW as Dr. Birx pointed out, the number of known cases was rise sharply as the number of tests increases. Testing is still an issue, but it won't be an issue for long.
The S&P 500 futures index dropped 100 points shortly after today's new conference began, about 3.7%.
Trump did the best thing possible and left the room after saying only a few words and leaving it all to people who are competent, articulate and who care.
13 comments:
Ned - I moved this response up from a question you asked in a prior thread.
Of course each presidential term is not the same. So what?
It's not that these terms differ. It's that they are not independent samples from the same, identical distribution. All these these statistical tests are based on this assumption.
People are taught statistical formulas without being taught the conditions under which each formula is valid. For better or for worse, these statistical formulas are very widely used when the proper circumstances do not exist. Even professional researchers all too often ignore this requirement. As a result, they get wrong results. This is a big issue today in the statistical community. Look up John Ioannidis for more info.
The next judgment is this: given that one's data doesn't match the [implicitly] assumed conditions, how close is it? IMHO, this variable -- Stock Market growth during a Presidential Term -- is not close at all to independent, identically distributed data. Therefore, there's no validity to measuring Dem vs Rep using these statistical formulas.
DiC: That's all just assertions. You simply declare that the data are not iid and imply that the departure from iid is severe enough to matter. But you don't show it.
I could come up with some rationales/arguments for why they might not be iid. Is the departure large enough to matter? Shrug.
David Appell: Thanks for the new chart. Note that the WHO data for Italy seem to be the same as the Worldometers data but lagged by 1 day, and the WHO data for the USA seem to be a rough approximation of the Worldometers data for the USA but lagged by *2* days.
So the WHO data seems to show Italy 11 days ahead of the USA, while the Worldometers data shows Italy ahead by 10 days.
Here is another version of your chart, based on the Worldometers data, and with the cases log-transformed:
https://i.imgur.com/5tyj5i6.png
It's scary how closely the USA is following Italy. Note also the blue dashed line, which is the trend for the USA data. A linear trend in the log-transformed data would be constant exponential growth. So far it's quite linear, but over the next 10 days Italy's rate seems to be slowing down a bit (dropping below the trend line). Is that due to the adoption of control measures? Or inadequate testing once the numbers get too big? Or that testing was lagging behind and caught up, after which the growth rate appeared to slow? Or the virus starting to reach some natural limit to its growth?
I am curious whether the USA will stay on that line, or start to drop below it like Italy. Increased testing in the USA could lead to an apparent increase in the rate. Widespread adoption of social distancing could slow it.
Of course on a per-capita basis, the case counts in the USA are 5x lower than what this indicates. They're still growing at the exponential rate, but it would be longer before we have the same density of cases. It looks like on a per-capita basis, the USA is 16-17 days behind Italy, depending on whether you use the Worldometers or WHO data.
From an outside perspective you seem to have a problem.
https://www.bbc.co.uk/news/world-us-canada-51875871
With an inept and ineffective federal government, through 51 states to 300 million individualists, you seem to be finding it difficult to decide on a common policy and a coordinated response.
But I should have done this graph per capita, for a better comparison. (I think.) Busy today, maybe later.
Here's the graph of USA vs Italy, cases per capita (actually per million), with a 16-day lag for Italy:
https://i.imgur.com/lwL67HO.png
and the same thing, but including the next 16 days (for Italy only, due to the 16-day lag):
https://i.imgur.com/gfmv07w.png
But I prefer the natural log transformed version:
https://i.imgur.com/2n9IsSW.png
The US trend has been very closely following an exponential growth function, which appears linear on the natural log version above. Extrapolating that to late March would give approx 1230 cases per million, or 400,000 cases total, in the USA.
However, Italy's rate of increase seems to be slowing. If the US follows the same path, it would be more like 100,000 cases nationwide.
I hope our newfound interest in social-distancing helps, and we bend the curve downward to stay below 100,000 cases in March.
I hope our newfound interest in social-distancing helps, and we bend the curve downward to stay below 100,000 cases in March.
It looks like testing is ramping up. That will help as well.
USA has tested about 20,000 on march 15th, and is now testing a few thousand a day.
Canada has tested about 23,000, and is now testing a few thousand a day, but we are hitting some issues ramping up to the levels needed. I expect USA will surpass us in a day or so.
My mom has been sick with a cough for weeks. They haven't tested her, but don't believe she has it. She's pretty vulnerable right now either way.
Schools and libraries are closed. Businesses are going online only. We'll know in two weeks whether this is enough to stem the tide.
L: Remember, though, there is a factor of 8.8 in population difference. So in effect Canada has done about 10 times more testing than the US.
PS: Per capita, Canadian case numbers are running at 73% of the US's.
But that was this morning. At 1 pm there were about 950 new cases in the US compared the same time yesterday, a one-day increase of about 40%. Deaths were up about 15%.
PPS: Best wishes to you mom.
Today's press conference with Trump and Pence and the health experts was encouraging. Starting tomorrow, the number of tests will be going up like a rocket. BTW as Dr. Birx pointed out, the number of known cases was rise sharply as the number of tests increases. Testing is still an issue, but it won't be an issue for long.
Cheers
The S&P 500 futures index dropped 100 points shortly after today's new conference began, about 3.7%.
Trump did the best thing possible and left the room after saying only a few words and leaving it all to people who are competent, articulate and who care.
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