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I need to compare an average value for an experimental group ($n=5$) with a reference value given by legislation.

But this reference value in given as [min - max] range.

Do I have to compare my average (with SD) with the two extremity of the range or could I use the mean value of the range ?

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    $\begingroup$ It depends on what you mean by 'compare'. What is the actual question you wish to answer? If you're comparing with the ends, you may wish to consider doing that as two one-sided tests. $\endgroup$
    – Glen_b
    Commented Aug 30, 2014 at 16:43
  • $\begingroup$ I need to know if my value (the average of 5 measurement repetitions) is inside the range given by "norm" with the adequate significance level. $\endgroup$
    – Terenz
    Commented Aug 30, 2014 at 17:35
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    $\begingroup$ The average of 5 measurement repetitions is a number you know; there's nothing to test, you just see if it's in the range. Hypothesis tests are for inference about population parameters not sample statistics. $\endgroup$
    – Glen_b
    Commented Aug 30, 2014 at 17:43
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    $\begingroup$ This could be regarded as an interval-censoring situation. I.e., you could use some sort of survival-analysis software to fit a model where the data have, say, a normal distribution with a certain mean structure (regression specs), but the actual values are unobserved and you only know they lie in an interval. $\endgroup$
    – Russ Lenth
    Commented Aug 30, 2014 at 18:16
  • $\begingroup$ @Glen_b and Russ Lenth Thank! Probably there is a misunderstandig in my last message. I will not repeat 5 times the measurement of the same "sample" (soil) but I'll measure 5 different "aliquots" of the sample. $\endgroup$
    – Terenz
    Commented Aug 31, 2014 at 10:33

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Since you are doing these analyses to compare your real world observations with legislated comparison values, you should do two analyses (one using the minimum and one with the maximum, as stated in the legislation). This approach provides maximum information to the person who has to make a decision, be that a manager or an attorney.

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  • $\begingroup$ thanks. So two "one-side" analysis for both sides of the range. $\endgroup$
    – Terenz
    Commented Sep 1, 2014 at 15:09
  • $\begingroup$ If the legislation calls for the value to be within the range, then 2 one-sided tests would make sense. $\endgroup$
    – Joel W.
    Commented Sep 1, 2014 at 15:43
  • $\begingroup$ Could I add a Complexity ? What could I do if the legislated values are expressed with mean value and SD ? $\endgroup$
    – Terenz
    Commented Sep 2, 2014 at 23:34
  • $\begingroup$ Is the intent of the legislation to describe a minimum, maximum, or what? $\endgroup$
    – Joel W.
    Commented Sep 3, 2014 at 0:05
  • $\begingroup$ sorry, it is a my complication and it could be meaningless. Probably it's better call it "reference value" instead of "legislated values" as in the main question. So, I'll rephrase my complication: How could I compare my sperimental value with a "reference value" expressed with mean value and SD ? the ref.value could be obtained from handbook, journal articles, etc. $\endgroup$
    – Terenz
    Commented Sep 3, 2014 at 19:59

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