some people are sure picky ... given the context in which the original post was made ... it seems like the audience that the poster was hoping to be able to talk to about CIs was not very likely to understand them very well ... thus, it is not unreasonable to proffer examples to get one into having some sense of the notion
the examples below ... were only meant to portray ... the idea that observations have error ... and, over time and over samples ... one gets some idea about what the size of that error might be ... thus, when projecting about behavior ... we have a tool to know a bit about some penultimate value ... say the parameter for a person ... by using AN observation, and factoring in the error you have observed over time or samples ... in essence, CIs are + and - around some observation where ... you conjecture within some range what the "truth" might be ... and, if you have evidence about size of error ... then, these CIs can say something about the parameter (again, within some range) in face of only seeing a limited sample of behavior At 09:30 PM 9/26/01 +0000, Radford Neal wrote: >In article <[EMAIL PROTECTED]>, >Dennis Roberts <[EMAIL PROTECTED]> wrote: > > >as a start, you could relate everyday examples where the notion of CI seems > >to make sense > > > >A. you observe a friend in terms of his/her lateness when planning to meet > >you somewhere ... over time, you take 'samples' of late values ... in a > >sense you have means ... and then you form a rubric like ... for sam ... if > >we plan on meeting at noon ... you can expect him at noon + or - 10 minutes > >... you won't always be right but, maybe about 95% of the time you will? > > > >B. from real estate ads in a community, looking at sunday newspapers, you > >find that several samples of average house prices for a 3 bedroom, 2 bath > >place are certain values ... so, again, this is like have a bunch of means > >... then, if someone asks you (visitor) about average prices of a bedroom, > >2 bath house ... you might say ... 134,000 +/- 21,000 ... of course, you > >won't always be right but .... perhaps about 95% of the time? > >These examples are NOT analogous to confidence intervals. In both >examples, a distribution of values is inferred from a sample, and >based on this distribution, a PROBABILITY statement is made concerning >a future observation. But a confidence interval is NOT a probability >statement concerning the unknown parameter. In the frequentist >statistical framework in which confidence intervals exists, >probability statements about unknown parameters are not considered to >be meaningful. you are clearly misinterpreting, for whatever purpose, what i have said i certainly have NOT said that a CI is a probability statement about any specific parameter or, being able to attach some probability value to some certain value as BEING the parameter the p or confidence associated with CIs only makes sense in terms of dumping all possible CIs into a hat ... and, asking .... what is the probability of pulling one out at random that captures the parameter (whatever the parameter might be) ... the example i gave with some minitab work clearly showed that ... and made no other interpretation about p values in connection with CIs perhaps some of you who seem to object so much to things i offer ... might offer some posts of your own in response to requests from those seeking help ... to make sure that they get the right message ... > Radford Neal > >---------------------------------------------------------------------------- >Radford M. Neal [EMAIL PROTECTED] >Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] >University of Toronto http://www.cs.utoronto.ca/~radford >---------------------------------------------------------------------------- > > >================================================================= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >================================================================= ============================================================== dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
