True negative decision

Type II error (beta error) An incorrect decision resulting from failing to reject the null hypothesis when the alternative hypothesis is true. A false negative decision. 

Baseline condition is true (H0 P > Ca) Correct decision The probability of making a correct decision (1—a) False acceptance decision error False negative decision error Type II decision error Probability ji Risk, error rate 100 x ft... 

Figure IS-4 Simulated distributions of healthy and diseased populations. Note that the ratio of diseased patients to healthy patients, A to B, is less than I and very different at the point of decision (the likelihood ratio) from the ratio of TP to FP, which is much greater than i. TP, True positives TN, true negatives FP, false positives FN, false negatives.

The Re-Os decay system is discussed separately, in part because there are far fewer osmium isotope data than Sr-Nd-Pb data. This is true because, until —10 years ago, osmium isotopes in silicate rocks were extraordinarily difficult to measure. The advent of negative-ion thermal ionization mass spectrometry has decisively changed this (Greaser et al., 1991 Vblkening et al., 1991), and subsequently the number of publications providing osmium isotope data has increased dramatically. 

Life is full of decisions, however, and so are Perl scripts. Often, there should be different paths followed if a particular condition is true, another if the condition is false. Considering the dog years calculator shown above, what would happen if the user had entered a negative number for the age or a number that s imreasonably large It would be desirable to reject the input outright, rather than produce and output a preposterous answer. This simple modification to the original script achieves this goal. 

Finally, following the enumeration of pathologic diagnoses, the choice of the statistical model can, in itself, affect the conclusion. This is especially true in discerning a negative from a weak positive effect. Thus, before we even approach the area of human risk assessment, or extrapolation, the complex test required to determine whether or not a chemical is an animal carcinogen, i.e., the basis for the qualitative decision, is already encumbered by many possible errors of procedure or judgment. 

Non-stationary demand patterns with independent realizations. When the statistical distribution of the demand in different periods varies, it is no longer true that a newsvendor solution of the type (10.9) is optimal, even if is replaced with Gf - the period-dependent distribution function of the lead time demand Di, The main reason for this is that in addition to the impact that the decision variable zt has on the expected cost at the end of period t, it may also have a negative consequence on the expected costs in later periods. Specifically, it may be the case that after placing the order Zt and after the demand Dt is realized, the inventory position at the beginning of period t + 1 will be higher than desired. It is easy to see that in the i.i.d. case, in which the target level /3 is fixed, this can never happen. 

To take into account the p error we must have resource to the new definition of the LOD CCp, the capability of detection " (as denoted by the EU) or minimum detectaljle net concentration, (as ISO termed it). This is the true analyte concentration that leads to a correct positive detection decision with sufficiently high probability (1 — jS). In other words, it is the minimum concentration of analyte that can be discriminated from the blank, controlling the risks of false positives and false negatives. 

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