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I conducted a survey where I asked respondents how much they reduced their financial overhead, based on the following options:

  • 0% (coded as 0 in my dataset)
  • 1-10% (coded as 1)
  • 11-25% (coded as 2, etc.)
  • 26-50%
  • 51-75%
  • More than 75%

My questions are these:

  1. Should I treat the responses like ordinal or interval data?
  2. If treated like ordinal and I calculate a median of say 1.5 (somewhere between 1-10% and 11-25% choices), how do I actually interpret a median of 1.5?

Because I am struggling to answer question #2, I am guessing treating this as interval data would be best.

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    $\begingroup$ This is certainly ordinal data. Note that being interval data is not a matter of values being intervals, but a matter of numerical codes allowing intervals between coded values to be treated literally (meaning, numerically). That's not so here, as (e.g.) (code 3 $-$ code 1) $\ne$ 2 (code 2 $-$ code 1) . If you treat your data as ordinal, it's possible that a program will report 1.5 as the median if half the values are 0 or 1 and half are 2 or more and the number of values is even. That's not to be taken any more literally than if 2.5 emerges as the median number of children across families. $\endgroup$ – Nick Cox Mar 17 '16 at 18:54
  • $\begingroup$ If only the (arbitrary) codes is what at your disposal then it is obviously ordinal data. But if you remember the real intervals behind it, as you showed, and can replace the codes by the percentage (say, mid-interval points), then your data is binned/censored interval. Please read the info in tag "ordinal". $\endgroup$ – ttnphns Mar 17 '16 at 20:11
  • $\begingroup$ Thank you both. @ttnphns, if I were to use the mid-interval points of the ranges (e.g., 1-10% becomes 5.5%, 11-25% becomes 18%, and so on), is it then acceptable to use the typical interval-level analysis tools (mean, standard deviation, etc.), with a caveat of course that the values are estimates? $\endgroup$ – Jake Mar 17 '16 at 21:49
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    $\begingroup$ You could treat your data as interval-censored rather than simply ordinal. $\endgroup$ – Glen_b -Reinstate Monica Mar 18 '16 at 0:00
  • $\begingroup$ Jake, Yes, you may consider and use binned (censored) variables as interval. $\endgroup$ – ttnphns Mar 18 '16 at 1:54

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