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From |
"Michael Blasnik" <[email protected]> |

To |
<[email protected]> |

Subject |
st: Re: RE: when your sample is the entire population |

Date |
Fri, 18 Jan 2008 16:30:39 -0500 |

I would just say -- "what Nick says" ;)

But I'd like to emphasize one aspect related to his points 3 (and/or 4) -- measurement error. In many real applications, the outcome (and, unfortunately, the predictors) are measured with error. Therefore, you have uncertainty even with data for the full population. Also, the superpopulation concept ( point 1) seems quite reasonable -- at least for most program evaluation questions where you may collect data for all program participants (or kids in a school) but they can be considered a sample of some larger potential population. Of course in program evaluation you also still have uncertainty introduced by any comparison/control group employed in the analysis.

Michael Blasnik

----- Original Message ----- From: "Nick Cox" <[email protected]>

To: <[email protected]>

Sent: Friday, January 18, 2008 3:02 PM

Subject: st: RE: when your sample is the entire population

I guess most people will have a short answer and a long answer to this one. You are going to get my short answer. Also, in statistical science, it seems that most people who think they have a reasonably smart, or at least sensible, answer think some of the other guys' reasonably smart answers are really fairly stupid, or at least difficult to understand. So it may be colourful if and when people start telling me that after a few decades of sweat and toil I _still_ don't understand statistics at all. If the question is what meaning is attached to a P-value, then there seem many possible partial answers. 1. I am looking only at a sample of size n and I think of this as only one of many possible samples of the same size from a larger population. That is most plausible if someone really did select that sample using random numbers, or something equivalent, and it's a greater or lesser stretch otherwise. In many cases the sample you have just fell into your lap somehow and the whole exercise is to treat the data _as if_ it were a random sample, partly because that's a calculation you can do. There's usually some wishful thinking involved. Both texts and teachers vary enormously on how candidly they discuss what is going on. This seems to be what is most emphasised in most introductory courses and texts, but it may be the least applicable story in statistical practice! 2. I am looking at a sample of size n and I am willing to think of this as one possible outcome among many. I can get a reference population by resampling the data I have repeatedly. Permutation and bootstrap methods fit under this heading. I think it wry that in less than 30 years bootstrap methods have gone from being widely regarded as a form of cheating to being widely considered as the best way to get a P-value in many problems. 3. I have a model, at its simplest response a function of predictors plus some error term, and the uncertainty comes from the fact that the model is always a approximation and stochastic by virtue of its error term. Whether your n is the whole N is immaterial, because the uncertainty is not about sampling at all. 4. What I have I regard as the realisation of a stochastic process (usually in time, or space, or both). The realisation is unique, but at least in principle there could have been other realisations. I won't quarrel with anyone who thinks #3 and #4 sound the same. 5. Bayesians have other stories. 6. I must have forgotten or be unaware of yet other stories. Bill Gould has tried to explain quantum mechanics to me several times. I am pretty clear that he understands it very well. In these terms you seem to be saying #1 does not apply in your case, but that still leaves other arguments, and there is a lot of scope for arguing what is central to #1 in any case. Nick [email protected]

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**Follow-Ups**:**Re: st: Re: RE: when your sample is the entire population***From:*David Greenberg <[email protected]>

**st: RE: Re: RE: when your sample is the entire population***From:*"McKenna, Timothy" <[email protected]>

**References**:**st: when your sample is the entire population***From:*Lloyd Dumont <[email protected]>

**st: RE: when your sample is the entire population***From:*"Nick Cox" <[email protected]>

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