How to convert indices into percentiles relative to sample sizes?

[Matthew Williams]

Hi all,

I am conducting a comparative study and I want to make the outcome comparable across countries. In my field (sociology), one of reference papers used this approach: "To provide a metric common across countries, we
convert the index scores into percentiles relative to the sample of all adults aged 60 and over in each survey". Unfortunately, I do not fully understand what they did and I would be grateful if someone can guide me how to do it. The followings are data examples of two countries. The outcome is score.

Country 1

clear
input float(id score) int age
  1 4 73
  2 5 81
  3 4 62
  4 6 75
  5 6 74
  6 4 77
  7 6 61
  8 0 61
  9 6 72
 10 1 64
 11 3 75
 12 0 60
 13 3 68
 14 0 62
 15 0 65
 16 2 65
 17 4 71
 18 0 61
 19 1 77
 20 2 81
 21 3 81
 22 4 66
 23 4 82
 24 3 62
 25 4 85
 26 5 70
 27 6 65
 28 6 67
 29 5 64
 30 0 81
 31 4 81
 32 4 60
 33 1 81
 34 6 80
 35 0 70
 36 8 60
 37 8 64
 38 8 65
 39 2 67
 40 4 70
 41 5 74
 42 3 92
 43 5 65
 44 5 72
 45 4 87
 46 2 70
 47 8 67
 48 6 85
 49 2 70
 50 0 68
 51 2 65
 52 0 77
 53 4 70
 54 4 62
 55 5 65
 56 5 71
 57 4 80
 58 2 63
 59 9 85
 60 3 75
 61 6 72
 62 1 62
 63 2 71
 64 6 69
 65 4 61
 66 2 62
 67 4 63
 68 2 66
 69 6 66
 70 4 61
 71 3 70
 72 3 65
 73 6 72
 74 1 69
 75 3 60
 76 4 71
 77 0 82
 78 8 60
 79 4 73
 80 6 87
 81 4 60
 82 1 71
 83 5 82
 84 3 75
 85 1 71
 86 1 62
 87 3 62
 88 4 62
 89 1 64
 90 0 78
 91 2 62
 92 2 61
 93 4 61
 94 4 63
 95 5 67
 96 4 63
 97 6 73
 98 5 69
 99 6 79
100 2 70
end

Country 2

clear
input float(id score) int age
  1 4 73
  2 5 81
  3 4 62
  4 6 75
  5 6 74
  6 4 77
  7 6 61
  8 0 61
  9 6 72
 10 1 64
 11 3 75
 12 0 60
 13 3 68
 14 0 62
 15 0 65
 16 2 65
 17 4 71
 18 0 61
 19 1 77
 20 2 81
 21 3 81
 22 4 66
 23 4 82
 24 3 62
 25 4 85
 26 5 70
 27 6 65
 28 6 67
 29 5 64
 30 0 81
 31 4 81
 32 4 60
 33 1 81
 34 6 80
 35 0 70
 36 8 60
 37 8 64
 38 8 65
 39 2 67
 40 4 70
 41 5 74
 42 3 92
 43 5 65
 44 5 72
 45 4 87
 46 2 70
 47 8 67
 48 6 85
 49 2 70
 50 0 68
 51 2 65
 52 0 77
 53 4 70
 54 4 62
 55 5 65
 56 5 71
 57 4 80
 58 2 63
 59 9 85
 60 3 75
 61 6 72
 62 1 62
 63 2 71
 64 6 69
 65 4 61
 66 2 62
 67 4 63
 68 2 66
 69 6 66
 70 4 61
 71 3 70
 72 3 65
 73 6 72
 74 1 69
 75 3 60
 76 4 71
 77 0 82
 78 8 60
 79 4 73
 80 6 87
 81 4 60
 82 1 71
 83 5 82
 84 3 75
 85 1 71
 86 1 62
 87 3 62
 88 4 62
 89 1 64
 90 0 78
 91 2 62
 92 2 61
 93 4 61
 94 4 63
 95 5 67
 96 4 63
 97 6 73
 98 5 69
 99 6 79
100 2 70
end

[Nick Cox]

I'd start at https://ideas.repec.org/p/bss/wpaper/37.html and see if that helps.

[Matthew Williams]

I'd start at https://ideas.repec.org/p/bss/wpaper/37.html and see if that helps.

Thank you Nick for the reference, the paper is really interesting. However, it seems what I am looking for is not listed in the paper. By the way, do you have any ideas of how to do the convert procedure stated in #1?

[Nick Cox]

Sorry: if that's not it, I don't have a different suggestion and like you I don't find the wording transparent. Why not give the exact reference?

[Matthew Williams]

Sorry: if that's not it, I don't have a different suggestion and like you I don't find the wording transparent. Why not give the exact reference?

Dear Nick,

The paper a I mentioned in #1 can be reached at: https://www.sciencedirect.com/scienc...77953615003019. However, it is behind a paid wall. If you can access the paper then please look for last paragraph in page 109 or you can do a quick searching with keyword "The psychological wellbeing index". Hope that you may find the paper interesting.

Thank you.