How to deal with the cases when participants gave rating of 2.5 or 4.5 on a 1-5 scale?

Because this was done during the interview, the participants just spoke out their rating rather than marked it done on the paper: they sometimes say "I think it is between 2 and 3" or "I give it 4 or 5". I want the rating to fully represent their thinking, and that's why I put 2.5 and 4.5. I don't know whether it is legitimate though.

So the question is:

In the cases when participants gave rating of 2.5 or 4.5 on a 1-5 scale, shall I change it to an integer when performing non-parametric test? If so, how shall I do the adjustment? 2.5->3?? or 2.5->2??

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Why not leave it as 2.5? –  Peter Flom Nov 29 '12 at 17:48
I tended to leave it as it is, but don't know whether it is legitimate. For nonparametric test which requires ordinal scale, is the non-integer good to work with in spss? –  Julie Nov 29 '12 at 17:52
It's still ordinal. If you like, you can multiply everything by 2, it will then be integer and still ordinal –  Peter Flom Nov 29 '12 at 18:20
What are you testing? Conceivably, how you treat these data depends on the test. After all, your 2.5 represents a range (or interval) 2-3, which is not quite the same thing as something between 2 and 3. Such a response can be an indicator of differences among subjects and perhaps deserves to be explored on that basis alone. Treating these responses as true ranges also suggests you could perform sensitivity analyses: if your test has the same outcome no matter what value you assign to each range, then the question is moot, but if its outcomes vary, you need to be careful. –  whuber Nov 29 '12 at 18:36

If people frequently felt that a 5-point scale was not sufficiently fine-grained, you could map this to a 9-point scale:

1   -> 1
1.5 -> 2
2   -> 3
2.5 -> 4
3   -> 5
3.5 -> 6
4   -> 7
4.5 -> 8
5   -> 9

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Thanks a lot, everyone!I now understand better the problem:) I meant to treat this rating as ordinal, which is discrete...but 2.5, 4.5 actually made it continuous in a sense, yeah, it is conflicting. So still this should remain ordinal and discrete,so I think mapping it into a 9-point scale can be a good solution. 1 -> 1 1.5 -> 2 2 -> 3 2.5 -> 4 3 -> 5 3.5 -> 6 4 -> 7 4.5 -> 8 5 -> 9 –  Julie Nov 30 '12 at 16:02

One option is to leave the rating as a 2.5 and run the analysis for an ordinal scale. The key characteristic of an ordinal scale is that the values are assumed to have a certain order without necessarily representing an additive increment (which they would in an interval scale) or a ratio increment (which they would in a ratio scale). Your treatment of the scale values as ordinal data merely assumes that 2 < 2.5 < 3 without assuming that the distance of 0.5 between points represents an interval or ratio increment.

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