Should I use a Weighted Average? HELP!

#1
Hi All - first post here and advanced warning I'm no stats wiz, but need the kind help of y'all. I have a huge dataset I am working with and trying to find something of significance...so far nada...but then I had a thought!

I am evaluating response rates of countries to letters sent by the UN, however some countries get many more letters than others, so its seems unfair to say one country has perfect compliance when they only have received 1 letter, whereas another country may have lower compliance but have received 500 letters.

My statisticians out there, any thought on how to develop a fairer way of evaluating compliance based on response rate, while factoring in the sheer quantity of letters received?

Here is a small sample dataset:

State Sent Replies Response Rate
Austria 1 1 100%
Croatia 1 1 100%
Czech Republic 6 6 100%
Estonia 1 1 100%
Finland 1 1 100%
Greece 8 8 100%
Hungary 10 10 100%
New Zealand 5 5 100%
Norway 3 3 100%
Portugal 4 4 100%
Slovakia 2 2 100%
Switzerland 6 6 100%
Uruguay 1 1 100%
Moldova 23 22 96%
Chile 18 17 94%
Canada 13 12 92%
Australia 23 21 91%
Spain 25 22 88%
Netherlands 8 7 88%
Costa Rica 7 6 86%
United Kingdom 25 21 84%
Sweden 6 5 83%
Bulgaria 5 4 80%
Ireland 4 3 75%
France 17 12 71%
Bosnia and Herzegovina 3 2 67%
Denmark 3 2 67%
Germany 3 2 67%
Paraguay 9 6 67%
Cyprus 8 5 63%
Tunisia 16 9 56%
Italy 13 7 54%
Botswana 4 2 50%
Lithuania 2 1 50%
Peru 18 8 44%
Panama 14 6 43%
Latvia 1 0 0%
Montenegro 1 0 0%
Poland 2 0 0%
Romania 4 0 0%

Disclaimer: this is for a thesis I am writing and will happily credit you all for you help!!! Thank you thank you thank you!!
 
#2
you could find the overall rate of compliance to letters, and then set some metric of weighting based on the mean. Such that, each successive letter after the first is given a progressively larger weight of probability for compliance.

i could provide a bit more detail but it might be mathematically sound, but it might not have any theoretical basis in your field.


Conversely, you can omit those countries who do not have at least x letters (where x is some arbitrary number that you set that is hopefully based in the literature of your field).
 
#3
You could divide your sample of countries into different groups based on the intensity of the outreach; for example, setting thresholds based on the number of letters sent, e.g., 1-8, 9-16, 17-24 - and call those Low, Medium, and High Intensity Outreach. Then compute the response rates for each and interpret and report them within each of their more comparable groups, rather than as part of the whole list.