Stastistics

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.

If I could spell statistics correctly that would help too.

@eladar said
People say, Stats, that's math. I say, not really.

You've shot yourself in the foot with that one cowboy!

@eladar said
If I could spell statistics correctly that would help too.

Also, revisit the “confidence interval” part. You have it backwards.

@joe-shmo said
Also, revisit the “confidence interval” part. You have it backwards.

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?

@venda said
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?

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.

@joe-shmo said
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.

Not according to stats. You have it wrong, but stats and other areas of math often disagree.

@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.

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.

@eladar said
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.

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.

@venda said
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?

If 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.

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.

@joe-shmo said
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.

Let me reword that.

It is not true that the number you are looking for is in the interval 95 percent of the time.

@eladar said
Let me reword that.

It is not true that the number you are looking for is in the interval 95 percent of the time.

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."

@joe-shmo said
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."

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.

@eladar said
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.

Well, 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:

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). "