It seems to me that Stastics is a field that not really understood very well by many people. People say, Stats, that's math. I say, not really.
For one thing Stats never says anything is true. When you use a stastical model you are not actually finding actual true answers. When you find a 95 percent confidence interval, the answer will not be in that interval 95 percent of the time.
In stats the best you can do is say, well this is probably right.
Stats is a different cat.
03 Apr 20
@eladar saidYou've shot yourself in the foot with that one cowboy!
People say, Stats, that's math. I say, not really.
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03 Apr 20
@eladar saidAlso, revisit the “confidence interval” part. You have it backwards.
If I could spell statistics correctly that would help too.
03 Apr 20
@joe-shmo saidDon't know what a confidence interval is but if I say(example only) 20% of my current chess games on red hot pawn are in the 7:14 time frame bracket and the evidence shows this to be true, are you saying that is not a statistic?
Also, revisit the “confidence interval” part. You have it backwards.
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03 Apr 20
2 edits
@venda saidA confidence interval of a certain size ( say 95% ) is a range of values where you would expect 95% of all data collected to be inside. For a "normal distribution" the 95% confidence interval is the Mean + or - two standard deviations. He has said the opposite by accident I suppose.
Don't know what a confidence interval is but if I say(example only) 20% of my current chess games on red hot pawn are in the 7:14 time frame bracket and the evidence shows this to be true, are you saying that is not a statistic?
03 Apr 20
@joe-shmo saidNot according to stats. You have it wrong, but stats and other areas of math often disagree.
A confidence interval of a certain size ( say 95% ) is a range of values where you would expect 95% of all data collected to be inside. For a "normal distribution" the 95% confidence interval is the Mean + or - two standard deviations. He has said the opposite by accident I suppose.
03 Apr 20
@joe-shmo
From Wiki
In statistics, a confidence interval (CI) is a type of estimate computed from the statisticsof the observed data. This proposes a range of plausible values for an unknown parameter (for example, the mean). The interval has an associated confidence level that the true parameter is in the proposed range.
03 Apr 20
In stats you never know if something is true, just likely. It is possible that in a random sample your data overwhelmingly comes from one end of the curve. If this happens it is possible that the true mean is is not captured.
A 95 percent confidence interval is an interval that will actually contain the number you want 95 percent of the time.
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03 Apr 20
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@eladar saidElader, This is your original post! I added the bold to emphasize your error.
In stats you never know if something is true, just likely. It is possible that in a random sample your data overwhelmingly comes from one end of the curve. If this happens it is possible that the true mean is is not captured.
A 95 percent confidence interval is an interval that will actually contain the number you want 95 percent of the time.
"When you find a 95 percent confidence interval, the answer will not be in that interval 95 percent of the time. " - Eladar
If you are having trouble seeing this, please carefully compare this and your wiki. quote.
03 Apr 20
@venda saidIf you are looking at all of your games, then no that is not a statistic. A statistic is based on knowing only some sample. If you have everything, then you have a census and is true by simple observation.
Don't know what a confidence interval is but if I say(example only) 20% of my current chess games on red hot pawn are in the 7:14 time frame bracket and the evidence shows this to be true, are you saying that is not a statistic?
Stats are used when you only know a part of the story and you want to know what is likely to be true of the entire story.
03 Apr 20
@joe-shmo saidLet me reword that.
Elader, This is your original post! I added the bold to emphasize your error.
"When you find a 95 percent confidence interval, the answer will not be in that interval 95 percent of the time. " - Eladar
If you are having trouble seeing this, please carefully compare this and your wiki. quote.
It is not true that the number you are looking for is in the interval 95 percent of the time.
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03 Apr 20
@eladar saidFrom The wiki you posted
Let me reword that.
It is not true that the number you are looking for is in the interval 95 percent of the time.
"Given observations x 1 , … , x n , and a confidence level γ a valid confidence interval has a γ probability of containing the true underlying parameter."
"For example, if the confidence level (CL) is 90% then in hypothetical indefinite data collection, in 90% of the samples the interval estimate will contain the true population parameter."
03 Apr 20
@joe-shmo saidThat is what I said. You are only using one sample, not knowing if the sample is a good one or a bad one.
From The wiki you posted
"Given observations x 1 , … , x n , and a confidence level γ a valid confidence interval has a γ probability of containing the true underlying parameter."
"For example, if the confidence level (CL) is 90% then in hypothetical indefinite data collection, in 90% of the samples the interval estimate will contain the true population parameter."
95 percent confidence interval, you have a 95 percent chance of having a correct interval but a 5 percent chance you will have an incorrect interval. You just do not know if the sample you have is part of the 95 or part of the 5.
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03 Apr 20
2 edits
@eladar saidWell, then it is some misunderstanding. It seems as though we are mixing and matching the use of the terms Confidence Interval and Confidence Level. Under the Interpretations Section:
That is what I said. You are only using one sample, not knowing if the sample is a good one or a bad one.
95 percent confidence interval, you have a 95 percent chance of having a correct interval but a 5 percent chance you will have an incorrect interval. You just do not know if the sample you have is part of the 95 or part of the 5.
https://en.wikipedia.org/wiki/Confidence_interval#Meaning_and_interpretation
"If the true value of the parameter lies outside the 90% confidence interval, then a sampling event has occurred (namely, obtaining a point estimate of the parameter at least this far from the true parameter value) which had a probability of 10% (or less) of happening by chance."
To me that sounds like if we have calculated a 90% Confidence Interval, we expect to find successive measurements within that Confidence Interval 90% of the time.
Then according to the Misunderstandings:
"Confidence intervals and levels are frequently misunderstood, and published studies have shown that even professional scientists often misinterpret them.[8][9][10][11][12]
A 95% confidence level does not mean that for a given realized interval there is a 95% probability that the population parameter lies within the interval (i.e., a 95% probability that the interval covers the population parameter). "