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I have two databases which include amount of passengers between two routes. One is the full dataset, while the other is supposedly a 10% sample.

So for example, the full database will display a route (AB)= 4.000 passengers while the 10% sample should display route (AB) = 400, obviously. However that doesn't always happen, but I still want to be able to validate with a certain confidence interval how much can my 10% sample variate.

I've been looking at different methods but so far bootstrapping for example doesn't seem to fit here as I can't figure out how to resample my route info. Meaning that I can resample the routes but then I'll have an absurd number for a certain route.

Edit: About the last paragraph. From what I understand from bootstrapping, I would resample the amount of passengers traveling on those routes. However, this is a fixed number meaning that there's no shuffling. The only resampling I could do would involve attributing a new value for the amount of passengers on route AB. For example resampling those numbers would either be based on the other routes, meaning that I could end with a number of 1 or 5 million. Or I would just resample that value based on a percentage which then I'm not sure how it would allow me to validate the 10% sample.

Saying so, I'm not sure how to validate if a 10% sample is indeed a 10% sample as there are no characteristics on the routes being analysed. It's just a sum of passengers, without any other characteristics.

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  • $\begingroup$ Your last paragraph is not clear to me. What is the obstacle you are facing? What is "absurd"? $\endgroup$ – rolando2 Mar 1 '18 at 12:53
  • $\begingroup$ @rolando2 I've added some more info. The problem is that I basically have to show that the 10% sample is representative, and indeed 10%. Meaning that it falls into a confidence interval (lets say 99%) of what would be possible to be a 10% sample. $\endgroup$ – FilipeTeixeira Mar 1 '18 at 13:23
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You could use a one way chi-squared analysis. Suppose you have 5 routes and their proportions of the total data set are .3, .3, .2, .1, .1. In your sample, suppose you get 100, 100, 70, 30, 25. Then, in R:

props <- c(.3, .3, .2, .1, .1)
samp <- c(100, 100, 70, 30, 25)
chisq.test(samp, p = props)

tests the hypothesis that the proportions in sample are equal to those in the population.

Similar methods are available in SAS and probably most other statistics packages.

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