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- From: barnett@mummy.agsm.unsw.OZ.AU (Glen Barnett)
- Subject: Re: Inferences from ratios verses differences
- Message-ID: <1993Jan11.051941.7476@usage.csd.unsw.OZ.AU>
- Sender: news@usage.csd.unsw.OZ.AU
- Nntp-Posting-Host: mummy.agsm.unsw.oz.au
- Organization: The Australian Graduate School of Management
- References: <1992Dec29.161137.20735@news.weeg.uiowa.edu>
- Date: Mon, 11 Jan 1993 05:19:41 GMT
- Lines: 80
-
- In article <1992Dec29.161137.20735@news.weeg.uiowa.edu> jfmurray@news.weeg.uiowa.edu (James F Murray) writes:
- >I have a question on the use of ratios verses differences for statistical
- >inferences. The situation is that we have two ordinal measures from patients
- >in several hospitals. For each patient we have a match between score on
- >admission and a score on discharge. We want to compare the change in patients
- >from admission to discharge across hospitals.
- [ stuff deleted ]
- >Our choices for comparison are to take the ratio of the admission/discharge
- >score for each individual patient (the ratio has to be formulated this way
- >because of the possibility of a 0 admission score)
- >OR
- >to take the difference between the two individual patient scores
- >(admission - discharge).
- >
- >I believe that the difference score should be used
- >and tested by nonparametric methods. My colleague resists using
- >the difference because of uncertainty about the effect on reliability and
- >power to detect differences.
-
- So why should a ratio not suffer from "uncertainty about the effect
- on reliability and power to detect differences" to at least as bad
- an extent?
-
- >
- >Any suggestions or pointers to literature on a comparison between
- >difference and ratio measures would be greatly appreciated.
- >
- It seems to me a matter totally related to measurement scale:
-
- A ratio seems appropriate when the items are measured on a ratio
- scale. The ratio of items measured on a ratio scale has a meaning.
-
- A difference seems appropriate when dealing with items on an
- interval scale. The difference between items measured on an
- interval scale has a meaning. The ratio of items measured
- on an interval scale is totally meaningless, in general.
- For example:
- If I calculated the ratio of (Farenheit) temperatures
- in Sydney for today and yesterday, and get .7, and take the same ratio
- for LA and get .91, what does that tell me about the comparison between
- Sydeny and LA? Well, the temperature went down in both cases, but that's
- about all I can say.
-
- If I calculated the differences, and got -19 for Sydney and -20 for LA
- (perfectly possible with the above ratios!), I can at least say the change
- in temperature was about the same for the 2 cities.
-
- Your data is on an *ordinal* scale. So if one person is admitted
- with a '3' and discharged with a '4' they get an admission-discharge
- of -1. If admitted with a zero and discharged with a '1' they get the
- *same* -1. Yet is the difference between a '3' and '4' the same as
- between '0' and '1'? I doubt it (if it was, you have an interval
- scale, not an ordinal scale).
-
- So your difference scores may not be totally meaningful, except as far
- as direction. That is, what you can say, is either the result
- went up, or went down, or stayed the same. This is another
- (coarser) ordinal scale. You could, for example, compare
- two treatments with this approach using a sign test, adjusted
- for ties (the ties occur when there is no change in category).
-
- However, if you say the differences are still meaningful (essentially
- asserting an interval scale rather than just ordinal), then
- you could use the differences to test and be able to speak
- meaningfully about the results.
-
- However, I can't see how you can ascribe any meaning whatever
- to the *ratios*. What is the point of testing anything on
- meaningless quantities?
-
- Just as an indication, someone who comes in with a zero
- will get a ratio of 0 NO MATTER WHAT SCORE THEY GO OUT WITH.
- Is that sensible? Are they really "the same"?
-
- Glen
-
- P.S. Issues of power and reliability seem secondary: If the quantities
- are meaningless, what good is power or reliability ? I contend that
- unless your test is appropriate to the scale the data were measured
- on, concepts like power have no meaning either.
-