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Comparing Quantities With Uncertainty Notes

The ter m agr eement means somet hi ng if the

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Unformatted text preview: ng to t he same physi cal quanti t y agree. The ter m “ agr eement ” means somet hi ng •If the measured If unc including the r one or b ot h num from random sources ver y sp eci fi c in an ex p er i ment . quantityer t ai nti es founcertainty calculated b er s (ex pr essed by an associ at ed σ) have b een cal culfaerror does not n say that another expected value (eitherwi t h another her if t hey over l ap ted, one ca overlap with the t wo numb er s agr ee from each ot o wit hin t heir uncer t aint ies. For exampl e, if a t heor y pr edi ct s that t he densi t y of an ob ject shoul d b e 10.0± 0.1 g/ cm3 , anxperimentsorrtheory) thenes a can ue of 9.that 0.3systematicthen we can say t he t wo val ues e d a mea u ement gi v you val assume 8± the g/ cm 3 , error in the agr ee wi t hi n t he ex p er i mental uncer t ai nt y. But if the measur ement gave inst ead 9.81 ± 0.02 g/ cm 3 , then we woul d b e experiment dominates at the t wo val ues di d not agr ee. for ced t o admi t ththe experimental error In t he case of di s•Thisemespecially exp er i menter faces a pr otheoretically t effect s have not b een accounted agr e is ent, t he true when comparing against bl em: whacalculated values, as for ? T here coul d b e a sour ce of addi t i onal random er r or that has not b een appr eci at ed, or mor e the theory almost always assumes some simplifications in order to make the vex i ng, t her e may b e a sour ce of syst emat ic er r or t hat is foul i ng t he accuracy of the measur ement . Gener al l y, sour ces cof random er r or ar e easi er to neglecting wn weightrect i fy ; but assuming i ng, one may alculation reasonable (for example, t r ack dothe and of a string or in so do uncover ot her sour ce...
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