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Presume I'm given a data set like Titanic, where the data on all the passengers is available (hence "population-encompassing" in the title). Then, by inertia, I proceed to conduct statistical inference on it by either:

  • Fitting a logistic regression, and only interpreting the effects with low p-values; or
  • Just conducting a two-sample proportion test, e.g. for survival rates of men vs women.

I have a plethora of questions on this type of practice for such non-randomly selected data set, that also appears to capture data on all the subjects (because I believe tons of people were doing it without even thinking much about the whole [sample => population] aspect of inference):

  1. My initial thought is, given that the data on all passengers is already available, the whole purpose of statistical inference (going from sample to population) is sort of eliminated, so why do the tests/calculate p-values?

  2. In case I proceed to do those tests though, is there any reasonable statistical explanation for their intended purposes? E.g. could I consider all Titanic passengers as a sample (convenience sample, I would guess), and then conduct inference on some larger population of subjects?

  3. If answer to 2 is yes, then what population would that be? E.g. other potential shipwrecks (which is doubtful, given that our sample is extremely biased towards just one ship)? Or an imaginary series of simulations for that Titanic shipwreck with potentially new passengers or something? I know I'm really grasping at straws here, but I would really like to know if there's a proper interpretation behind something that a lot of people do on those types of data sets almost automatically (conduct those tests, interpret p-values etc).

  4. Is it reasonable to justify use of p-values with a question along the lines of "but how else do we check if this non-zero effect wasn't just due to chance"?

  5. If inference is nonsensical here, should one simply go by the practical sizes and interpretations of the observed effects?

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I'll try for a combined answer. If you have entire population data in a very strict sense, the idea of drawing inferences on population's distribution parameters lose sense of course.

However, in titanic data for example, full data does not mean population data. The population can be defined based on the analysis you are doing on data. For example, if you are checking the attributes that helps you guess chances of survival in an accident like Titanic then that's what your population becomes: potential victims of Titanic like accident.

There's another dimension to this, I think (I am not fully sure of this though for discrete random variables). Say an individual is defined by 10 attributes. In the population no two individual are such that they have 9 same attributes but one different (call this attribute x). How do you compute the impact of attribute 'x' on chances of survival. If the population is complete such an analysis does not make sense at all. However hypothetical if such two individuals were to exist, how would the chances of survival differ? Regression might help to give an answer to this question.

Thoughts?

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    $\begingroup$ (+1) this is basically it. I'll elaborate on a couple points. 1) thank you for explicitly thinking about your sample and population. Dayne noted you might want to extrapolate to similar disasters; you might also think of a hypothetical population like "people who might have been on the Titanic." If you had been on the Titanic, how confident are you that you would have surivived? 2) regression can tell you how attributes of people on the ship were related to their survival, though inference on regression coefficients must involve a hypothetical larger population. $\endgroup$ – Sheridan Grant Aug 26 at 7:07

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