Type II 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. 

In this light, the type II error is a hypothetical entity, but very useful. A graphical presentation of the situation will help (see Figure 1.34). 

False negative responses of 0.13-3.2% are an acceptable price. What are the chances of false positives slipping through Four alternative hypotheses are proposed for the VVV scheme (compare p to SL = 99.0, with p = j3, the type II error ) ... 

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. 

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 not safe and effective but the approval system approves it, because it is not sufficiently demanding with the proof it requests. We will call this a type II 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. 

Landau M., Stout. Jr. R., 1979. To manage Is Not To Control Or the Folly of Type II Errors, Public Administrative Review March April, pp. 148-156. 

The wrong acceptance of a false hypothesis leads to committing a type II error. The probability of a type II error is designated ft and (1 — j8) is called the power of the test. For a certain Hi, it is not possible to make both a and ff arbitrarily small. Decreasing the probability of one type of error increases the probability of the other and vice versa. The balance between both types of errors depends on the purpose of the test. 

The screen must be very sensitive in its detection of potential effective agents. An absolute minimum of active agents should escape detection that is, there should be very few false negatives (in other words, the type II error rate or beta level should be low). Stated yet another way, the signal gain should be way up. 

I, the probability of our committing a type II error (a false negative) ... 

Independent variables P-value Power Also known as predictors or explanatory variables Another name for significance level usually 0.005 The effect of the experimental conditions on the dependent variable relative to sampling fluctuation. When the effect is maximized, the experiment is more powerful. Power can also he defined as the probability that there will not be a Type II error (1-/1). Conventionally, power should be at least 0.07... 

Type II Error (false negatives) Concluding there is no effect when there really is an effect. Its probability is the beta level... 

If the power function is denoted by [3(9) and H0 specifies 6 = 60, then the value of /3 (II), the probability of rejecting H0 when it is in fact valid, is the significance level. A test s power is greatest when the probability of a type II error is the least. Specified powers can be calculated for tests in any specific or general situation. 

This type of error equates to box C and is variously described as a type II error, a false-negative error or the 6 error. A type II error in a study result would lead to the incorrect acceptance of the null hypothesis. 

Another important aspect is to ensure that we limit the errors in drawing the wrong conclusion. These are described as Type I and Type II errors ... 

Type II Error (P, False Negative) The probability of wrongly concluding that there is no difference when in fact there is a difference, which means keeping a good medicine away from patients, with the manufacturer missing an opportunity to market the drug. Type II error is normally limited to 5-20% (i.e., P = 0.05-0.2). The boundaries of Type II error are normally set by the company. 

Once the parameters for the hypothesis and Type I and Type II errors are set, the total number of subjects (IN) to be recruited to join the trial can be determined by the equation... 

Beta (p) Is the probability of calling a polluted panel clean or the type II error and shown as dotted area to the left of CV In Figure 1. 

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. 

Note that If beta equals alpha, beta Is one fourth of the traditionally allowed type II error (l.e.,. 05 Instead of. 20). This shows that the unthinking use of textbook examples or traditional confidence levels can be dangerous to the environment and public health. Pollution monitoring statistics must have Its own beta calculations. 

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

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