IzzyR: it is clear that you are operating under two large misconceptions, namely:
Simply insulting other people is an effective rebuttal to their arguments.
Taking a high school statistics course, or reading the Cartoon Book of Statistics, or whatever you did to gain your limited understanding of statistics, somehow gives you the standing to contradict someone who actually understands the theoretical underpinnings of statistics (and releases you from the obligation of defending those contradictions with anything more than your arrogance).
I’d provide an explanation of your most recent misunderstandings, such as your claim that “But as a practical matter, as with a gambler who gives odds on the results of a coin toss that has already been tossed, there’s no difference,” but it has become clear to me that you are not interested in rational discourse. If there is anyone who sincerely wants to know about real statistics, as opposed to this bastard form which IzzyR has been parading around, let me know.
Strange juxtaposition. I guess you not only pay no attention to what others are writing - you pay no attention to what you yourself are writing either.
And here I thought I was being nice to you. Okay…
Was that the problem? Okay. dorkbro alluded to nothing of the sort.
The “probability of getting a range that includes the true value” will clearly be the same as the probability that the same range, once you got it, actually includes the value. It’s incredible that anyone would think it’s worthwile to pretend otherwise. Any distinction is only with regards to whether the mathematical term probability can still be applied to this likelihood.
It does? Oh.
The preceding exchange was very enlightening, but, unfortunately, only regarding how limited are your understanding of the topic and willingness to discuss it. More about that later.
So as to have you come away from this debate with something positive, I will explain to you a little about the principle of scientific standards, including significance levels.
Supposing a statistician sets the significance level for a given test at 95%. This means that the null/alternative hypothesis will be accepted/rejected should the level of probability rise above 95%. This does NOT mean that the scientist has determined by some scientific method that at 95% some magic line will have been crossed and the results will suddenly become significant. The difference between 94.9% and 95.0% is not inherently more significant than the difference between 73.3% and 73.4%. It is a marginal difference. However, a test must have some standard. There must be some point at which one draws the line between pass and fail. And different test must have some degree of commonality to their standards, so as to be able to compare the results of one test against another. For this reason certain common significance levels have come into practice.
However, in reality, there is no point that is suddenly “significant”. Returning to the OP; if I am a political candidate, or a supporter of one, and I am recieving poll results, I am not concerned about the difference between a 94.9% likelihood of being ahead and a 95% likelihood, even though one may be at, and one below, the significance level. I am very concerned about the difference between a 62% likelihood of being ahead and a 94.9% likelihood, even though both are below the significance level. Anyone who says otherwise, a group that apparently includes you, is a fool or a liar.
Interesting thing is that throughout your several “contributions” to this thread you have completely limited yourself to mistaken interpretations of what others have said. The years you have spent studying advanced statistics have not been evident.
So let’s see what you’ve got, Mr. “someone who actually understands the theoretical underpinnings of statistics”. Say something of intelligence. Specifically, explain the difference between the “probability that the true value lies within the indicated range”, and “the probability of getting a range that includes the true value”, in a manner that has some relevence, in some way, to this thread. Provide an explanation of my “most recent misunderstandings”.
Oh, I forgot. You can’t respond to me because, unlike yourself, I am “not interested in a rational discourse”. In other words, you’re in over your head.
What led you to that conclusion? Do you think that I was trying to substitute an insult for an argument? I had already shown that you were wrong, and saw no need, or point, to providing further proof, and I made no claim, explicit or implicit, that I was doing so.
This is you being nice?
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Careful analysis of your latest post reveals that you are under the mistaken impression that your previous post was not completely silly.
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That’s your opinion.
The first phrase refers to the proportion of an entire class of ranges that contain the true value. The latter refers to a single range. Just what makes you think that a single range will have the exact same properties as the class from which it came has as a whole? Do you have any reasoning that went into this conclusion? Or is it just something that you just decided “must” be true?
It doesn’t to you.? You hear the level of certainty, and then you decide whether that level of certainty is good enough.
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Supposing a statistician sets the significance level for a given test at 95%. This means that the null/alternative hypothesis will be accepted/rejected should the level of probability rise above 95%.
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Well, you have it backwards; unless the statistician really wants to reject the null, the significance level would be 5%, and the null would be rejected if the probability went below 5%. But this is a minor point compared to your other mistakes.
This does NOT mean that the scientist has determined by some scientific method that at 95% some magic line will have been crossed and the results will suddenly become significant. The difference between 94.9% and 95.0% is not inherently more significant than the difference between 73.3% and 73.4%. It is a marginal difference. However, a test must have some standard. There must be some point at which one draws the line between pass and fail. And different test must have some degree of commonality to their standards, so as to be able to compare the results of one test against another. For this reason certain common significance levels have come into practice.
A clarification: I have been using the term “significant” in its statistical meaning. In common language, significance is indeed a subjective term, and there is no clear dividing line. However, in statistics “significance” has a very clear meaning: it is whatever the statistician decides at the beginning of the test it will be. This initial decision is indeed arbitrary, but after that the matter of whether a result is significant is very cut and dry There is nothing subjective or arbitrary about it.
I never said that you are not concerned more about the difference between 62% (should be 38%) and 94.9% (should be 5.1%) than you are about the difference between 94.9% (should be 5.1%) and 95% (should be 5%). I’m simply saying that if the test has a significance level of 5%, then a 5% result is significant, and a 5.1% result is not. A 5.1% result may be more impressive to you than a 38% result, but the 5.1% result isn’t any “less non-significant” than the 38% result; they are both non-significant.
That’s a rather ironic statement, considering that I have identified several instances of you misunderstanding what I have said, but you have not identified a single such instance on my part.
Here’s the correct way of constructing a 95% confidence interval. First, you decide what test you’re going to perform, and what statistic(s) you are going to gather. In the case of a political poll, the standard statistic is the sample mean, that is, the percentage of people who support some position or candidate. Now, you decide on a formula based upon that statistic that will yield a range. Now, your statistic can have many different values, and each one of these will yield a different range, so there are many different possible ranges. The probability of getting each range depends upon the true mean, which we have no way of knowing. So we have to set up our formula so that no matter what the true mean is, the probability of getting a range that includes that mean is 95%. This may seem difficult, but it is simplified by the covention that “95%” is usually taken to mean “at least 95%”; if you say that you have a 95% chance of getting the right value, not very many people are going to complain if you actually have a 96% chance.
So the probability of getting a range which includes the correct value is the proportion of all possible ranges that include the correct value, which is usually set to be more than or equal to 95%. Since there are usually an infinite amount of ranges, this number is usually continuous. The probability of the correct value in the indicated range is the proportion of correct values which are in the indicated range. Since there is only one correct value, this proportion is always one or zero.
How does the fact that you are not interested in rational discourse indicate that I am over my head?
What I really don’t understand about this thread is that the newscasters are, in essence, declaring the possibility of error to be too likely to make a definite declaration. Why do you consider yourself qualified to tell these people what they should consider too likely?
The range will not necessarily have the exact same properties as the class which it came from. But the likelihood of it’s containing a value is one that it will. You have failed to show otherwise, for obvious reasons.
Just in case there is a small possibility that there is some genuine confusion on this issue, that was not the meaning of that statement.
This, my freind, is very basic stuff. In fact, I disctinctly remember learning about this in “The Cartoon Book of Statistics” that you refer to. What no amount of obfuscating will blur (at least I hope not), is the fact that it is irrelevent to the discussion here. As I wrote earlier “as a practical matter, as with a gambler who gives odds on the results of a coin toss that has already been tossed, there’s no difference”. You called this my “latest misunderstanding”. You have not clarified this at all.
It is very obvious that you have been using the term in this context. It is equally obvious, or should be, that the entire point of this post is to decry the confusing use of a statistical scientific term when the statistical scientific aspects of it are not well understood or relevent.
Uh, I’ll have to help you a bit with this one.
In the course of this lengthy debate, which included much unpleasantness in each direction, there is one distinction between us. I was for the most part actually saying something; you, by contrast limited yourself to critisisms (and attempting to replay dorkbro’s remarks). You did not make an attempt to actually explain your position on how things actually were, you merely stated that I had it wrong for this or that reason. The first time you actually posted something of any substance was your most recent post, and this was only after some prodding from me. And then, even though it took you quite a long time to come up with, the stuff you wrote was actually quite basic, introductory level statistics.
It has therefore been, and still is, my conviction, that when you made your initial post to this thread you had not paid much attention to what you were actually commenting on. You probably have some vague grasp of statistics, and have probably learned it on a basic level at some point in your past. This has unfortunately given you a false confidence that you know more that most on the subject, and when you saw a thread that discussed these matters without alot of technical jargon you assumed that the poster was someone who knew nothing (or at least alot less then you) of the subject. You therefore posted some condescending remarks without bothering to pay full attention to the issues that were actually being discussed. Then, once you ended up in the position of having to defend remarks that made no sense in context, and in a field that you have only a vague grasp of, you responded by avoiding anything that actually addressed the subject matter.
As I write this, I am trying to consider if it is at all possible that I wronging you, and I certainly apologize if this is the case. But I honestly can’t see it.