0

Dear all I'm looking for some help and confirmation since it's been a while since I have done these types of calculations.

I'm trying to calculate a few things with regards to populations. I want to have them weigthed on 2 or maybe 3 types of criteria, such as life expectancy, percentage of total population, amount of income, and maybe some other factors.

Normally with only 1 criteria/weight I know how to do this and it would be fairly easy.

By example for life expectancy, I could sum the life expectancy of each age group I take, giving me a total amount of life expectancy over all the age groups. I could then divide the value of each age group by the total give me a percentage or fraction of 1.

Basically $\sum_{i=0}^n (w_i \cdot x_i)$ or $\frac{\sum_{i=0}^n (v_i \cdot x_i)}{\sum_{i=0}^n v_i}$

However this is only for 1 criteria. If I start multiplying fractions (percentages) I won't get the right number and only smaller and smaller fractions not adding up to unity.

This for 2 weights would then be incorrect $\sum_{i=0}^n (w_1i \cdot w_2i \cdot x_i)$ With w being the weighted fractions.

What would be the best way to handle this and are there any "standard/common" equations or methods for this?

Unfortunately my first Google searches and math stack exchange didn't show me any useful results. (Keep in mind I might not have searched using the correct terms as it has been a while)

Bob van de Voort
  • 157
  • It is not clear what you want. If you have multiple factors which you want to scale under, you have to declare how you want to compare things. If, say, a subject is $1\sigma$ up in one variable and $1\sigma$ down in another, how should that be weighted against a subject that hits both means exactly? And so on. That's not a math question...the answer will depend on how you plan to use the data. – lulu Dec 30 '20 at 16:48
  • Just assume that per category I know what the fraction per age group is. A subject is not going to have multiple agesvor belong to multiple age groups. So by example if I say the age categories are below 60 and those that are 60 and older. Then I would know that by example 20% is older and 80% is younger. So the weight/fraction for the younger part is 0.8 and the older parts is 0.2 – Bob van de Voort Dec 30 '20 at 17:04
  • But, again, you speak of multiple criteria, so you need to say something about how you intend to weight those relative to each other. Is your goal to use a, potentially biased sample, to predict data for an unbiased sample? But then you will want to match "buckets"...people in some range for criterion 1, some range for criterion 2, and so on. – lulu Dec 30 '20 at 17:21
  • Hmmm okay thanks for the clarification. Well the buckets per criterion will always be over the same range as I can get the necessary data for that. I might be misunderstanding something. A good example would calculating the left over life expectancy of the entire current population. Where I need to take into account which fraction there's per age and the expected rest life expectancy per age. These are 2 criterion in that case (this is not your simple life expectancy). – Bob van de Voort Dec 30 '20 at 18:12
  • I should say: it is extremely difficult to "remove" bias from a sampling pool. That one reason national polls can be so wildly inaccurate. You never know which external variables matter, nor how they interact. Some of the relevant buckets tend to be so sparsely populated that you end up magnifying pure noise. It's a big mistake to imagine that there are simple, standardized tricks that get you past all these problems. – lulu Dec 30 '20 at 18:16
  • It's not about removing bias never did I say so. That's an assumption you're making. – Bob van de Voort Dec 30 '20 at 19:07
  • I have no idea what you are trying to do. You never said, so I made some assumptions. You are free to edit your post to explain what your goal is. – lulu Dec 30 '20 at 19:09

0 Answers0