Rejection false

Interpretation While good batches of the quality produced (= 99.81% purity) have a probability of being rejected (false negative) less than 5% of the time, even if no replicates are performed, false positives are a problem an effective purity of /.t = 98.5% will be taxed acceptable in 12.7% of all cases because the found Xmean is 99% or more. Incidentally, plotting 100 (1 - p) versus /x creates the so-called power-curve, see file POWER.xls and program HYPOTHESlS.exe. 

The relationship between the risk, a, of falsely rejecting the null hypothesis and the level of confidence, P, placed in the alternative hypothesis is P = 100(1 - a)%. If the null hypothesis is rejected at the 87% level of confidence, what is the risk that the null hypothesis was rejected falsely ... 

Accounting for its purpose, every significance test has to be designed individually A medical test should always warn the patient in case of a severe disease on the other hand, establishing a result by means of statistics, a test should preferably reject false positive results. These antithetic demands are represented by the terms of sensitivity and specificity ... 

A critical attribute of a successful chemical sensor is its ability to reject false alarms from background interferent vapors. Sensors that false alarm frequently, whether it be daily, weekly, or even monthly, tend to be ignored with time as the personnel monitoring the devices assume that each new alarm is a false alarm. Sensors which false alarm less frequently (perhaps only once a year or less) tend to be taken more seriously. 

Maximum entropy reconstruction [32] is claimed to remrn a maximally noncommittal solution. It calculates a small set of proposed S Fi,F maps that are compatible with the measured projections within the experimental errors, and selects the one with the least information content. For this reason it suppresses all noise and artefacts in the reconstruction and is therefore prone to be misleading. In another terminology, it rejects false positives but is likely to return false negatives . This particular feature suggests that the maximum entropy solution could prove to be a useful starting point for more sophisticated statistical programs. 

Truth Builders must use honest and true materials—erafted by human hands, not machines—respecting them and rejecting false ones. 

The second type of error occurs when the null hypothesis is retained even though it is false and should be rejected. This is known as a type 2 error, and its probability of occurrence is [3. Unfortunately, in most cases [3 cannot be easily calculated or estimated. 

Risk-Based Inspection. Inspection programs developed using risk analysis methods are becoming increasingly popular (15,16) (see Hazard ANALYSIS AND RISK ASSESSMENT). In this approach, the frequency and type of in-service inspection (IS I) is determined by the probabiUstic risk assessment (PRA) of the inspection results. Here, the results might be a false acceptance of a part that will fail as well as the false rejection of a part that will not fail. Whether a plant or a consumer product, false acceptance of a defective part could lead to catastrophic failure and considerable cost. Also, the false rejection of parts may lead to unjustified, and sometimes exorbitant, costs of operation (2). Risk is defined as follows ... 

Several nontechnical factors can significantly affect the results of a nondestmctive inspection. Many of these are classified as human factors (1,2,17). Operator experience affects the probabiUty of detection of most flaws. Typically, an inexperienced operator has more false rejects, known as Type II errors, than an experienced operator. A poor operator has few false rejects but is more likely to miss a defect in the inspection, known as a Type I error. Operator fatigue, boredom, or an unfavorable environment such as lighting, cold, or rain may further affect performance. Thus it usually is a good investment for the inspection company to assure that the operator environment is most amenable to inspection, that the equipment is suitable for the task, and that the operator is alert and well rested. 

The use of the older restricted version of the Pauli principle has persisted, however, and is routinely employed to develop the electronic version of the periodic table. Modern chemistry appears to be committing two mistakes. Firstly, there is a rejection of the classical chemical heritage whereby the classification of elements is based on the accumulation of data on the properties and reactions of elements. Secondly, modem chemistry looks to physics with reverence and the false assumption that therein lies the underlying explanation to all of chemistry. Chemistry in common with all other branches of science appears to have succumbed to the prevailing tendency that attempts to reduce everything to physics (11). In the case of the Pauli principle, chemists frequently fall short of a full understanding of the subject matter, and... 

Assuming one wants to be certain that the risk of falsely declaring a good batch B to be different from the previous one A is less than 5%, the symmetrical 95% confidence limits are added to A (see Fig. 1.22) any value B in the shaded area results in the judgment B different from A, Hi accepted, Hq rejected , whereas any result, however suspect, in the unshaded area elicits the comment no difference between A and B detectable, H rejected, Hq retained . Note that the expression A is identical to B is not used by statistical means only deviations can be demonstrated, and similarities must be inferred from their absence. 

The simultaneous test given by Equations 6 and 7 leads to a test appropriate for (X,t) unknown. The (X,T)-unknown test rejects the null hypothesis that xgj belongs to the background population if tj > c(r) for all (X,t). Since this test rejects the null hypothesis only if Equation 6 is satisfied for the true value of (X,t), this test has no greater probability of false detection than the simultaneous test. Thus, the (X,r)-unknown test is conservative in the sense that the probability of a false detection is less than a if the probability of false detection for the simultaneous test is a. 

To reject the null hypothesis erroneously although it is true (error of first kind, false-negative, risk a). 

Not to reject the null hypothesis by erroneously though the alternative hypothesis is true (error of second kind, false-positive, risk / ). 

Not rejected Test result OK Error of second kind consumer risk false alarm ... 

Rejected Error of first kind producer risk false alarm Test result OK... 

If an analytical test results in a lower value x, < x0, then the customer may reject the product as to be defective. Due to the variation in the results of analyses and their evaluation by means of statistical tests, however, a product of good quality may be rejected or a defective product may be approved according to the facts shown in Table 4.2 (see Sect. 4.3.1). Therefore, manufacturer and customer have to agree upon statistical limits (critical values) which minimize false-negative decisions (errors of the first kind which characterize the manufacturer risk) and false-positive decisions (errors of the second kind which represent the customer risk) as well as test expenditure. In principle, analytical precision and statistical security can be increased almost to an unlimited extent but this would be reflected by high costs for both manufacturers and customers. 

A test will not always lead to the right decision. It is possible that Ho is true and is rejected, or that Ho is false and is accepted. 

What we have been saying should not suggest to the reader the desirability of accepting uncritically evidence for the importance of genetics. We advocate instead that all phases of the subject be looked at with the same critical attitude, and that the evidence to be found in the field of genetics be given fair consideration and not be rejected a priori on the basis of false philosophical implications. 

This type of error equates to box B and is variously described as a type I error, a false-positive error or the a error. A type I error in a study result would lead to the incorrect rejection of the null hypothesis. 

This leads to the term Power (1 - j3), which quantifies the ability of the study to find the true differences of various values of S. It is the probability of rejecting the null hypothesis when it is false or determining that the alternative hypothesis is true when indeed it is true. 

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