This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
In the discussion of estimation of sample variance I don't believe we need the assumption of normality. Just iid will do will it not?
-- Richard Clegg 17:48, 10 Feb 2005 (UTC)
In my understanding, the mean square measure of "bias" of a given statistic is in fact a measure of it's expected power. It represents the variability of the statistic's sampling distribution. While this is an important factor to consider when choosing your statistic, it is not a measure of bias per se.
Thoughts?
Informavore aka Mike Lawrence 23:52, 24 March 2006 (UTC)
Trying to find the average weekly alcohol consumptions by the students at a highschool, you interview all the students. Results may skewed by some untrue answers - depending on the context, one could have deliberate exaggerations of the alcohol consumption, or the opposite, or respondents might give incorrect answers due to incomplete memories. Suppose, for example, that most students tend to exaggerate, leading to too high an average.
Would it be correct to describe this error as a bias? I'd say yes, the students are biased towards exaggeration, but this is neither due to a biased sample (we are asking the whole population), nor to a biased estimator (we are looking at simple averages).
Is this, then, a third type of bias that ought to be included in the article? Unlike the other two types, it is due to an error in each individual observation, not in the way they are bunched together. But all the same, it is a systematic error in a statistical investigation.-- Niels Ø 11:10, 27 October 2006 (UTC)
I am not on top of this theory; I haven't even read and understood everything in the article. However, I have doubts about the following example:
(My bolding.) Unless we have an a priori assumption about the distribution n, is it possible to have an unbiased estimator for n? Suppose we do not know n, but we know that it is either 100 or 1000, with equal probabilities. We observe X=17, and so conclude that we are not much wiser, but I guess it strengthens the possibility 100 slightly. Certainly 2X-1 = 33 is not an unbiased estimator. Or suppose we observe X=117; then we know n=1000, and 2X-1 is even worse. Is this a silly objection? I think not; we will always have a priori knowledge (such as: "n is not likely to be more than a million"), and I don't think you can show that an estimator is unbiased without quantifying a priori probabilities. So 2X-1 may possibly be called a natural estimator (whatever that is), but I don't think you can call it an unbiased estimator.-- Niels Ø 08:59, 5 November 2006 (UTC)
I suddenly get it; of course you are right. The way to see it is, n actually has some specific value (not a distribution), and the estimator 2X-1 has the expected value n, and hence it is unbiased. I was confused among other things because I had the following confusing (and only remotely connected) problem in mind: In a quiz program or something, you are presented with two envelopes. One contain a sum of money; the other one twice that sum. You are allowed to open one envelope (containng X), and then to choose which of the envelopes to keep. Without an apriori distribution, it would be tempting to say "the other" envelope has 50% chance of containing 2*X, and 50% for 0.5*X, giving an expected value of 1.25*X, so switching seems like a good idea. But the quiz program must have a limited budget, so if X = 10 000 000 dollars, perhaps you should stay with the envelope you opened. Or maybe not... Anyway, you should include an apriori distribution in your considerations. As far as I recall, it is discussed in a Martin Gardner book.-- Niels Ø 08:30, 8 November 2006 (UTC)
Could anyone start the article common-method bias? When started I will add some additional sections to that article. 78.53.34.179 ( talk) 13:38, 12 September 2010 (UTC)
The analytical bias article is gone, rotting a link in trial registration. Where should I link to for bias introduced by choosing your analytical methods after you've looked at the data? It is this bias which is prevented by requiring the registration of full trial protocols, as opposed to a mere announcement of a trial, so the article makes little sense without this information. Reporting_bias#Outcome_reporting_bias does not quite seem to hit the nail on the head. Thanks for any advice. HLHJ ( talk) 22:18, 3 July 2017 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
In the discussion of estimation of sample variance I don't believe we need the assumption of normality. Just iid will do will it not?
-- Richard Clegg 17:48, 10 Feb 2005 (UTC)
In my understanding, the mean square measure of "bias" of a given statistic is in fact a measure of it's expected power. It represents the variability of the statistic's sampling distribution. While this is an important factor to consider when choosing your statistic, it is not a measure of bias per se.
Thoughts?
Informavore aka Mike Lawrence 23:52, 24 March 2006 (UTC)
Trying to find the average weekly alcohol consumptions by the students at a highschool, you interview all the students. Results may skewed by some untrue answers - depending on the context, one could have deliberate exaggerations of the alcohol consumption, or the opposite, or respondents might give incorrect answers due to incomplete memories. Suppose, for example, that most students tend to exaggerate, leading to too high an average.
Would it be correct to describe this error as a bias? I'd say yes, the students are biased towards exaggeration, but this is neither due to a biased sample (we are asking the whole population), nor to a biased estimator (we are looking at simple averages).
Is this, then, a third type of bias that ought to be included in the article? Unlike the other two types, it is due to an error in each individual observation, not in the way they are bunched together. But all the same, it is a systematic error in a statistical investigation.-- Niels Ø 11:10, 27 October 2006 (UTC)
I am not on top of this theory; I haven't even read and understood everything in the article. However, I have doubts about the following example:
(My bolding.) Unless we have an a priori assumption about the distribution n, is it possible to have an unbiased estimator for n? Suppose we do not know n, but we know that it is either 100 or 1000, with equal probabilities. We observe X=17, and so conclude that we are not much wiser, but I guess it strengthens the possibility 100 slightly. Certainly 2X-1 = 33 is not an unbiased estimator. Or suppose we observe X=117; then we know n=1000, and 2X-1 is even worse. Is this a silly objection? I think not; we will always have a priori knowledge (such as: "n is not likely to be more than a million"), and I don't think you can show that an estimator is unbiased without quantifying a priori probabilities. So 2X-1 may possibly be called a natural estimator (whatever that is), but I don't think you can call it an unbiased estimator.-- Niels Ø 08:59, 5 November 2006 (UTC)
I suddenly get it; of course you are right. The way to see it is, n actually has some specific value (not a distribution), and the estimator 2X-1 has the expected value n, and hence it is unbiased. I was confused among other things because I had the following confusing (and only remotely connected) problem in mind: In a quiz program or something, you are presented with two envelopes. One contain a sum of money; the other one twice that sum. You are allowed to open one envelope (containng X), and then to choose which of the envelopes to keep. Without an apriori distribution, it would be tempting to say "the other" envelope has 50% chance of containing 2*X, and 50% for 0.5*X, giving an expected value of 1.25*X, so switching seems like a good idea. But the quiz program must have a limited budget, so if X = 10 000 000 dollars, perhaps you should stay with the envelope you opened. Or maybe not... Anyway, you should include an apriori distribution in your considerations. As far as I recall, it is discussed in a Martin Gardner book.-- Niels Ø 08:30, 8 November 2006 (UTC)
Could anyone start the article common-method bias? When started I will add some additional sections to that article. 78.53.34.179 ( talk) 13:38, 12 September 2010 (UTC)
The analytical bias article is gone, rotting a link in trial registration. Where should I link to for bias introduced by choosing your analytical methods after you've looked at the data? It is this bias which is prevented by requiring the registration of full trial protocols, as opposed to a mere announcement of a trial, so the article makes little sense without this information. Reporting_bias#Outcome_reporting_bias does not quite seem to hit the nail on the head. Thanks for any advice. HLHJ ( talk) 22:18, 3 July 2017 (UTC)