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Chemical Analysis Basics
Published in Thomas J. Bruno, Paris D.N. Svoronos, CRC Handbook of Basic Tables for Chemical Analysis, 2020
Thomas J. Bruno, Paris D.N. Svoronos
Statistically, the error rate is the frequency of type I and type II errors in null hypothesis significance testing. This has importance in forensic chemistry, for example, when the blood alcohol content (BAC) of a sample is measured. Here, a null hypothesis might be: the BAC of sample X is not below 0.08 % (mass/mass). A measurement above that level, and therefore a failure to reject the null hypothesis, can result in a legal finding of intoxication. A type I error occurs when a rejected null hypothesis is correct (false positive); a type II error occurs when the accepted null hypothesis is false (false negative). Independent of the frequency of type I and type II errors (the statistical error rate), each measurement of BAC has an uncertainty. The uncertainty of each measurement is determined by the propagation of the contributions to uncertainty that is represented by the uncertainty budget, multiplied by the appropriate coverage factor. The error rate of a particular laboratory or technique is not so easily determined. In some large state forensic laboratories, error rates can be approximated by inserting known standard samples anonymously into the normal workflow, but even this approach has limitations.
Statistical Inference I
Published in Michael Baron, Probability and Statistics for Computer Scientists, 2019
Probability of a type I error is the significance levelsignificance level of a test, α=P{reject H0|H0 is true}. Probability of rejecting a false hypothesis is the power of the testpower of the test, p(θ)=P{reject H0|θ;HA is true}. It is usually a function of the parameter θ because the alternative hypothesis includes a set of parameter values. Also, the power is the probability to avoid a Type II error.
Project Control System
Published in Adedeji B. Badiru, Project Management, 2019
Type I error refers to the rejection of the null hypothesis when it is true. Type I error is normally expressed in terms of a significance level denoted as α. That is, α=P(TypeIerror)=P(rejectingH0|H0istrue)
Gaussian Process-Aided Function Comparison Using Noisy Scattered Data
Published in Technometrics, 2022
Abhinav Prakash, Rui Tuo, Yu Ding
So far, our goal can be described as testing against the alternative hypothesis H1. We will propose a test method, so that its Type I error under has a probability controlled by a prespecified significance level α. Note that the Type I error under iswhere denotes the probability measure of the GP prior. It is worth noting that the Type I above is not identical to the Type I error under the original null hypothesis H0. However, we expect that the proposed method can serve as an approximate method for the fixed-function testing problems, and we will verify this expectation via numerical studies in Section 3.
Parameter determination and performance evaluation of time-series-based leakage detection method
Published in Urban Water Journal, 2021
Tuqiao Zhang, Xin Li, Shipeng Chu, Yu Shao
The accuracy of the test method is affected by two types of errors. In statistical hypothesis testing, a type I error means detecting a leakage scenario that is not present (a ‘false positive’), while a type II error means failing to detect a leakage scenario that is present (a ‘false negative’). Two types of errors can be quantitatively analyzed using Rate of False Alarm (RF) and Detection Probability (DP), respectively. The higher the DP, the higher the probability that the leakage scenario will be detected. The higher the RF, the higher the probability that the no-leakage scenario will be misjudged as a leakage scenario. The calculation formulas for DP and RF are as follows: Detection Probability (DP): the proportion of leakage scenarios detected in the total number of natural random leakage scenarios.Rate of False Alarm (RF): the proportion of false alarms in the total number of natural random scenarios that occur without a leakage.
Rotation of the thrower-discus system and performance in discus throwing
Published in Sports Biomechanics, 2021
Five critical instants in discus throwing procedure were identified as (1) right foot takeoff, (2) left foot takeoff, (3) right touchdown, (4) left foot touchdown, and (5) release of discus (Figure 2; Hay & Yu, 1995). Paired t-tests were performed to compare official distance and partial distances, and normalised system angular momentum and three direction cosines of whole-body angular momentum vector at right foot takeoff, left foot takeoff, left foot touchdown, and release between long and short trials. System angular momentum at right foot touchdown was not analysed because system angular momentum does not change during airborne between left foot takeoff and right foot touchdown. A Type I error rate less than or equal to 0.05 was chosen as the indication of statistical significance.