A nice answer says

A margin of error and a confidence interval are pretty much the same thing - it's the interval in which you are quite confident that the true parameter lies. If you have a 95% confidence interval, that means that if you were to repeat your experiment, 95% of the time the true parameter value would fall within your interval. Roughly speaking, there's a 95% chance that the interval contains the true value. The margin of error is simply describing the width of your confidence interval. So, if you have a confidence interval of [4, 6], you can say that your parameter estimate is 5 with a margin of error of 1.

where the term "true parameter" is used.

I am trying to understand that term. I searched a bit and got a post What, precisely, is a confidence interval?, which seems to talk about CI theoretically without a real life example, which is hard for me to understand.

Assume the U.S. Census Bureau published a survey of people in poverty in 1995. The survey stated a confidence level of 90% for the statistics “The number of people in poverty in the United States is 35,534,124 to 37,315,094.”

What the "true parameter" is in the example of Census Bureau's survey? Could someone please give a hint?

The example is adapted from source

  • $\begingroup$ Another of the many "confidence interval" meaning questions worth reading is stats.stackexchange.com/questions/26450/… $\endgroup$ – Henry Apr 7 '20 at 14:16
  • $\begingroup$ @Henry Thank you. 230 upvotes indicates that post is really worth reading. I will read it thoroughly and carefully when I get a clear understanding of the basic concept with some real life examples. Would you please recommend some discussion about CI with real life examples, e.g. poll, survey, screening some kind of disease? $\endgroup$ – WXJ96163 Apr 7 '20 at 14:26
  • $\begingroup$ @WXJ96163 it's an interesting request, but you seem to have enough top down exposure to statistics, what's seems to be lacking for you is a theoretical basis. I'm not sure if it's considered off-topic. $\endgroup$ – AdamO Apr 7 '20 at 15:17
  • $\begingroup$ This question appears to answer itself, because the phrase in the quotation "The number of people in poverty in the United States" describes the "true parameter." $\endgroup$ – whuber Mar 18 at 13:30

It seems the sticking point of the OP is the phrase "true parameter." In the referenced posts I see a lot of references to "population mean", which may aid understanding initially, until one realizes that "true parameter" and "population mean" do not coincide.

Here is an inarguable statement:

The data target the processes that produced the data.

In almost all situations, including the census, the processes that produced the data do not center on the "population mean," because of numerous biases and other deviations from pure random sampling.

So what one means by "true parameter" is instead a (assumed stable) value of the data-generating process, one which the data targets (or "aims at"). Only in the most pristine of data collection scenarios can this "true parameter" be called a "population mean."

  • $\begingroup$ Your "inarguable" statement looks suspect to me. I think we can all agree (because it's a tautology) that data reflect the processes that produced them. It's the word "target" that is bothersome. From the perspective of applying statistical analysis, the objective of a confidence interval is to make a statement about a property of the real world. Often, the "processes that produced the data" are distractions and annoyances; they are not of direct interest. It is also generally helpful to distinguish the ontological referent of "true parameter" from its meaning within a specific model. $\endgroup$ – whuber Mar 18 at 14:43
  • $\begingroup$ I don't like "reflect" in this context, because it suggests that the aim is elsewhere. My point is the data aim at whatever they aim at, yes, tautologically. So the parameter one constructs a confidence interval for may very well not be what they want, but that is realistically, what they get. $\endgroup$ – BigBendRegion Mar 18 at 15:06

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