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chl
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It is common practice in psychology to add together ordered items to sum-scores, and then use these sum-scores for subsequent statistics. This is usually done without explicitly mentioning measurement level, and I guess people simply assume items to be interval or ratio.

I wonder about this practice, and the implications. An example are screening instruments for mental disorders. Items are mostly ordered (and not interval or ratio), and a sum-score is used as threshold to determine whether someone has a disease or not.

Isn't it correct that for a sum to be meaningful, equidistant points between each of the scale elements would be needed, allowing for an interpretation of differences in the degree of order? Adding up the numbers 2, 2, and 3 to a sum-score only makes sense if the first 2 is equal to the second 2, and if the 3 is 1.5 times larger than each of the 2s (which is highly problematic with ordered items, obviously).

Is there (critical) statistical literature regarding that topic? What would be your opinion? I have looked for a while now but probably wouldn't even know the technical terms to look properly.

Thank you

It is common practice in psychology to add together ordered items to sum-scores, and then use these sum-scores for subsequent statistics. This is usually done without explicitly mentioning measurement level, and I guess people simply assume items to be interval or ratio.

I wonder about this practice, and the implications. An example are screening instruments for mental disorders. Items are mostly ordered (and not interval or ratio), and a sum-score is used as threshold to determine whether someone has a disease or not.

Isn't it correct that for a sum to be meaningful, equidistant points between each of the scale elements would be needed, allowing for an interpretation of differences in the degree of order? Adding up the numbers 2, 2, and 3 to a sum-score only makes sense if the first 2 is equal to the second 2, and if the 3 is 1.5 times larger than each of the 2s (which is highly problematic with ordered items, obviously).

Is there (critical) statistical literature regarding that topic? What would be your opinion? I have looked for a while now but probably wouldn't even know the technical terms to look properly.

Thank you

It is common practice in psychology to add together ordered items to sum-scores, and then use these sum-scores for subsequent statistics. This is usually done without explicitly mentioning measurement level, and I guess people simply assume items to be interval or ratio.

I wonder about this practice, and the implications. An example are screening instruments for mental disorders. Items are mostly ordered (and not interval or ratio), and a sum-score is used as threshold to determine whether someone has a disease or not.

Isn't it correct that for a sum to be meaningful, equidistant points between each of the scale elements would be needed, allowing for an interpretation of differences in the degree of order? Adding up the numbers 2, 2, and 3 to a sum-score only makes sense if the first 2 is equal to the second 2, and if the 3 is 1.5 times larger than each of the 2s (which is highly problematic with ordered items, obviously).

Is there (critical) statistical literature regarding that topic? What would be your opinion? I have looked for a while now but probably wouldn't even know the technical terms to look properly.

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Torvon
Torvon
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Summing up ordered items to a sum-score: implications?

It is common practice in psychology to add together ordered items to sum-scores, and then use these sum-scores for subsequent statistics. This is usually done without explicitly mentioning measurement level, and I guess people simply assume items to be interval or ratio.

I wonder about this practice, and the implications. An example are screening instruments for mental disorders. Items are mostly ordered (and not interval or ratio), and a sum-score is used as threshold to determine whether someone has a disease or not.

Isn't it correct that for a sum to be meaningful, equidistant points between each of the scale elements would be needed, allowing for an interpretation of differences in the degree of order? Adding up the numbers 2, 2, and 3 to a sum-score only makes sense if the first 2 is equal to the second 2, and if the 3 is 1.5 times larger than each of the 2s (which is highly problematic with ordered items, obviously).

Is there (critical) statistical literature regarding that topic? What would be your opinion? I have looked for a while now but probably wouldn't even know the technical terms to look properly.

Thank you