Qualified comments on possibly "fudged" statistics

[dcragoe]

I would like to get comments on some numbers from people qualified in statistics, if there are any on this forum. Others can comment also.
These are estimates for a certain subset of the population in different nations:

10,001,000 - seems like they took an estimate of 10,000,000 and added 1,000 to it, does it not? What is the chance that this is accurate, assuming the authors were estimating to the closest 1,000?

Here are some other numbers:
600,140
200,300
50,400

I'm curious if these numbers look "fudged" to other people on this forum.

[bokonon]

I would like to get comments on some numbers from people qualified in statistics, if there are any on this forum. Others can comment also.
These are estimates for a certain subset of the population in different nations:

10,001,000 - seems like they took an estimate of 10,000,000 and added 1,000 to it, does it not? What is the chance that this is accurate, assuming the authors were estimating to the closest 1,000?

Here are some other numbers:
600,140
200,300
50,400

I'm curious if these numbers look "fudged" to other people on this forum.
They're estimates, not counts, so aren't they "fudged" by definition?

[Dilb]

Having only 4 numbers, and no context, any statistical argument would be meaningless. If you had a few thousand numbers, and an explanation of how they were generated, then we could do some statistical tests for randomness, or possibly check to see if it follows Benford's law.

As it is, all I can say is that's a lot of zeros if it's supposed to be real-world data, but sometimes that happens.

[DevilsAdvocate]

I would like to get comments on some numbers from people qualified in statistics, if there are any on this forum. Others can comment also.
These are estimates for a certain subset of the population in different nations:

10,001,000 - seems like they took an estimate of 10,000,000 and added 1,000 to it, does it not? What is the chance that this is accurate, assuming the authors were estimating to the closest 1,000?

Here are some other numbers:
600,140
200,300
50,400

I'm curious if these numbers look "fudged" to other people on this forum.Does not look fudged. Looks rounded. The only thing that might look off is 10 million rounded to nearest 1 thousand, but 600 thousand is rounded to nearest ten. And 200 thousand and 50 thousand rounded to nearest 100. May or may not be inconsistent rounding. But no evidence of fudging.

[Towlie]

Does not look fudged. Looks rounded.In other words, they look like they have low precision.

But we don't know that. For all we know, those numbers were hand-picked from a larger list simply because of how they look. We were not given enough information to say anything more than that they are numbers.

[Modified]

If these are the only four large numbers in an academic paper, then I would suspect compounded rounding errors. For example:

100,000 (rounded) members of a population of 503,868 have property x.
100,000 / 503,468 = 20% (rounded)
later (and maybe in a different paper)
20% * 503,868 = 100,773.6 = 100,770 (rounded).

[Beth]

I would like to get comments on some numbers from people qualified in statistics, if there are any on this forum. Others can comment also.
These are estimates for a certain subset of the population in different nations:

10,001,000 - seems like they took an estimate of 10,000,000 and added 1,000 to it, does it not? What is the chance that this is accurate, assuming the authors were estimating to the closest 1,000?

You mean as opposed to 9,999,999? Or 10,243,000? Neither of them are any more likely than 10,001,000 or even 10,000,000. On the other hand, it's possible it's a typo and the estimate doesn't have that degree of accuracy. I think that the number one in the middle has a higher probability of being an error than the zero in the middle of 10,000,000 or the nine in the middle of 9,999,999.


Here are some other numbers:
600,140
200,300
50,400

I'm curious if these numbers look "fudged" to other people on this forum.

They look rounded to me. What do the numbers represent? What is the context in which they appear. Do other similar numbers display similar levels of accuracy?

[dcragoe]

Thanks for everyone's comments. These numbers from the British Fluoridation Society. They have an online booklet titled "One in a Million."
These are figures for population estimates of people in those countries with the "optimal" level of fluoride in their drinking water from a natural source. They gathered this data with the help from the Centers for Disease Control. The numbers have probably been reported by dentists or public health officials in those countries, so various methods were likely used to come up with the estimates. The numbers vary widely from some with lots of zeros (China with 200,000,000) to some with estimates down to the last person (Australia with 143,433)

They reported 10,001,000 in the United States as having the "optimal" fluoride level in their water from natural sources. It seemed to me like someone took an estimate of 10,000,000 and added 1,000 to it to make it seem more accurate. I'm a skeptic sometimes, and I think I have reasons to be that way here.

I naturally got suspicious when I added up the numbers for all the different nations on table 31 and got different totals than the British Fluoridation Society reported at the bottom of the table. I would appreciate it if anybody else would like to check this.

Using their data the British Fluoridation Society made this statement:
"Worldwide around 400 million people benefit from a fluoridated water supply, with the US being one of the most extensively fluoridated countries."

They used their data in a very questionable way, in my opinion. When they estimated the total number of people in the world with fluoridation, they left out China for some unexplained reason. They also did not include India on their data sheet at all. If you add their figure for China (200,000,000) to the number of people who "benefit from a fluoridated water supply" you get 600 million, and not 400 million as they state in their booklet. But perhaps they did not want to include China since the Chinese might not like being told they "benefit" from fluoride in water. Millions there are crippled by it. Millions more in India have the "optimal" level, but perhaps they did not want to participate in this survey for the same reason. Both India and China actively remove fluoride from drinking water, and never add it, except for formerly British Hong Kong. Both India and China do have large areas with "optimal" natural level of fluoride in water.

The British Fluoridation Society's convenient definition of the word "fluoridated" in their statement means both nations with artificial and natural "optimal" levels of fluoride in water added together. But that definition is not in the dictionary, and they do not let the reader know what they mean by it. By adding artificial and natural fluoride areas together they came to the figure of 400 million. But by leaving out India and China that figure is much smaller than it should be.

I think the American Dental Society is deceptive in their use of the British data. They currently state it is a "fact" that "Over 405 million people in more than 60 countries worldwide enjoy the benefits of fluoridated water" As you can see from the British data, there are only 31 nations that add fluoride to drinking water. The dictionary says "fluoridate" means to add fluoride. The American Dental Society also fails to define "fluoridated water" as including both artificial and natural in their "Fluoridation Facts" document.

Yes, this may be a battle over semantics and deceptive estimates, but there is a bit more to the story. In 2002, the American Dental Society said it was a "fact" that "60 nations practice water fluoridation." When I asked the ADA and the British Fluoridation society for a list of the 60 nations they were sure they were right but they could not provide a list of the 60. After this was publicized the British Fluoridation Society and the CDC went to work gathering data. And the result is chart 31 in "One in a Million." How do you "practice water fluoridation" when it's already in the water naturally?

Comments?