In statistics, if the null hypothesis is that all and only the relevant items are retrieved, absence of type I and type II errors corresponds respectively to maximum precision ( no false positive ) and maximum recall ( no false negative ).
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A Type I error would falsely indicate that treatment A is more effective than the placebo, whereas a Type II error would be a failure to demonstrate that treatment A is more effective than placebo even though it actually is more effective.
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In a study of the use of econometrics in major economics journals, null-hypotheses ) and neglect concerns of type II errors; some economists fail to report estimates of the size of effects ( apart from statistical significance ) and to discuss their economic importance.
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While both type I and type II errors are important in research situations, type one errors can have a therapeutic utility in clinical situations, in which they can provide an indirect opportunity for positive autosuggestion much like the indirect suggestions employed in Ericksonian hypnosis.
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* Mistake and Error are supposed to be synonymous to each other, but they portray certain differences in the light of statistical inference . describe in regards to type I and type II error . The preceding contribs ) 10 : 37, 18 April 2007 ( UTC ).
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The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis is true ( statistical significance ) and the probability of type II error is the probability that the estimator doesn't belong to the critical region given that the alternative hypothesis is true.
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Working from a null hypothesis, two basic forms of error are recognized : Type I errors ( null hypothesis is falsely rejected giving a " false positive " ) and Type II errors ( null hypothesis fails to be rejected and an actual difference between populations is missed giving a " false negative " ).
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"In statistics, a false negative, also called a Type II error or miss, exists when a test incorrectly reports that a result was not detected, when it was really present . ( Alternatively, a Type 2 error can be thought of as a failure by accepting the alternative hypothesis when the null hypothesis was truly false . )"
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Examples of type II errors would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease; a fire breaking out and the fire alarm does not ring; or a clinical trial of a medical treatment failing to show that the treatment works when really it does.
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Where the cost or impact of a Type I error is much greater than the cost of a Type II error ( e . g . the water is safe to drink ), it can be worthwhile to bias the decision-making system towards making fewer Type I errors, i . e . making it less likely to conclude that a particular situation exists.
