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A main limitation for reporting or measuring a percent reductions is having zero in the denominator. For example, if one was counting data on paired subjects and then analyzing the effects of some treatment before 'b' and after 'a' implementation. Putting study design assumptions aside, one could apply following expression:

100%*(1-a/b) = percent change or difference between before 'b' and after 'a' periods.

However, if there was zero observations in the before 'b' period the percent reduction would evaluate to negative infinity (ie 100%*(1-a/0)=-Inf).

my question is would it would be valid to replace the negative infinity (-Inf) with -100% in cases where counts in the before period 'b' were zero (ie 100%*(1-a/0)=-100). The justification is that the a/0=-Inf is the same measurement as 100 but in the opposite direction because it is its' inverse.

cn838
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    If the "before" value is zero, then percent reduction is meaningless. Imposing any value would be arbitrary and could adversely affect all follow-on analyses. – whuber Jul 31 '21 at 15:16
  • thanks, one must understand R outputs two different results when computing percent reduction (ie NA and -Inf). i just put a footnote that says 1-0/0= DIV/0! is zero change, and when b=0, the inverse (a/b)^-1 was computed. – cn838 Aug 02 '21 at 18:48

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