Type I error

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. 

Purpose Display the type I error (a) and the type II error (/3) both as (hatched) areas in the ND(/iREp, Urep) and the ND(/ttest, test) distribution functions and as lines in the corresponding cumulative probability curves. 

A problem long appreciated in economic evaluations, but whose seriousness has perhaps been underestimated (Sturm et al, 1999), is that a sample size sufficient to power a clinical evaluation may be too small for an economic evaluation. This is mainly because the economic criterion variable (cost or cost-effectiveness) shows a tendency to be highly skewed. (One common source of such a skew is that a small proportion of people in a sample make high use of costly in-patient services.) This often means that a trade-off has to be made between a sample large enough for a fully powered economic evaluation, and an affordable research study. Questions also need to be asked about what constitutes a meaningful cost or cost-effectiveness difference, and whether the precision (type I error) of a cost test could be lower than with an effectiveness test (O Brien et al, 1994). 

The Type I error is the error most often cited in the literature. In environmental monitoring, however, the Type II error may be more important. A false negative could create major problems for the environmental manager if it suggests that a cleanup is not necessary when in fact action levels are being exceeded. 

The drag is safe and effective but the approval system rejects it, because it demands more proof. We will call this a type I error . 

If a government tightens up its drug approval policy it will have fewer type II errors but more type I errors, and vice versa. Therefore, an ideal drag approval policy should take into account both the costs and the benefits of a stricter or less strict policy when approving a pharmaceutical. Insofar as the costs and benefits stated above are important factors in the decision to approve or reject a drug, the role of economic evaluation is clear. 

Growing experience with complex disease genetics has made clear the need to minimize type I error in genetic studies [41, 109]. Power is especially an issue for SNP-based association studies of susceptibility loci for phenomenon such as response to pharmacological therapy, which are extremely heterogeneous and which are likely to involve genes of small individual effect. Table 10.2 shows some simple estimation of required sample sizes of cases needed to detect a true odds ratio (OR) of 1.5 with 80% power and type I error probability (a) of either 0.05 or 0.005. 

On the other hand, the relative positions of the PC region and the ellipse are fixed under any chosen type I error, regardless of the structure of , thus leading to consistent performance. 

Wrongly rejecting a true hypothesis is referred to as committing a type I error. Its probability is designed by a, the significance level of the test. 

It is desirable that the number of false positives be small (i.e., there should be a low type I error rate or alpha level). 

Type I Error (false positives) Concluding that there is an effect when there really is not an effect. Its probability is the alpha level... 

If ANOVA reveals no significance it is not appropriate to proceed to perform a post hoc test in hope of finding differences. To do so would only be another form of multiple comparisons, increasing the type I error rate beyond the desired level. 

Duncan s assures a set alpha level or type I error rate for all tests when means are separated by no more than ordered step increases. Preserving this alpha level means that the test is less sensitive than some others, such as the Student-Newman-Keuls. The test is inherently conservative and not resistant or robust. 

The Scheffe procedure is powerful because of it robustness, yet it is very conservative. Type I error (the false positive rate) is held constant at the selected test level for each comparison. 

Dunnett s seeks to ensure that the type I error rate will be fixed at the desired level by incorporating correction factors into the design of the test value table. 

Portier, C. and Hoel, D. (1984). Type I error of trend tests in proportions and the design of cancer screens. Comm. Stat. Theory Meth. A13 1-14. 

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. 

Yang Q, Cui J, Chazaro I, Guppies LA, Demissie S. (2005) Power and type I error rate of false discovery rate approaches in genome-wide association studies. BMC Genet. 6(suppl 1), SI34. 

Increasing the sample size would reduce both alpha and beta, but samples and especially their analyses cost money. Intuitively the minimal actual loss should occur when the expected losses are equal. So the relative alpha and beta should be found from equating expected loss from type I error with the expected loss from type II error. 

P a (loss from type I error) (loss from type II error)... 

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