1
$\begingroup$

This is a very basic question, but I need help to grasp the concept. From what I understand:

  1. If I carry out a survey on body weight, every single answer to the question "How much do you weigh?" is a sample variable.

  2. Several sample variables form the sample vector.

  3. The sample function (e.g. mean) assigns such a sample vector a real number.

  4. The advantage of assuming that each observation is a sample variable is that the value which results from the application of the sample function is also a random variable, which permits the application of (axioms of) probability theory.

My question is this: Why is it not possible to apply probability theory based on the following:

  • Q1. A single sample of 30 observations is drawn. These 30 observations form the sample variable (vis-a-vis 1. and 2, this would be the pendant to the sample vector.).
  • Q2. Given that the 30 observations were drawn randomly, the sample function is also a random variable, which permits the application of (axioms of) probability theory.

Furthermore, is it not - again conceptually - "dishonest" to claim that there exist millions of sample variables, each of a particular body weight, instead of recognizing that "body weight" is a variable, of which these sample variables are really just particular realizations?

Am I making an issue of a non-issue?

Thank you!

$\endgroup$
  • $\begingroup$ So this question has been answered here: link. But perhaps someone could explain this using the above scenario (body weight) as an example to make it clearer in the concrete. $\endgroup$ – Spaniel19 Jan 4 at 9:29

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.