![]() 4 However, in many applications in chemometrics, we do not strictly define a hypothetical distribution but use a training set. One important issue is that most classical statistics deals with distributions: So a statistician may say that a sample comes from a hypothetical (usually parametric) distribution, often, but not exclusively, a normal distribution. The latter is calculated either using a hypothetical distribution or a training set, whereas the former may be calculated on a test set or any independent samples. There is some confusion in terminology between the type 1 error rate and the probability of a type 1 error (and also for type 2 errors). there would be 40 TPs, 10 FNs, 70 TNs and 30 FPs.Hence, if there were 50 positive samples of which a particular test predicted 40 of them correctly and 100 negative samples of which the test predicted 70 of them correctly The type 2 error happens when a sample is a false negative (FN).This is also called a probability of a type 2 error. ![]() The value β is defined as the proportion of sample or measurements that are part of the alternative distribution that are incorrectly predicted to be members of the null distribution.By the original definition, the probability of a type 1 error was calculated prior to performing experiments, using a given distribution or an experimental training set, and predetermined decision criterion.The type 1 error rate (α) is the probability as to how often this is expected. The type 1 error happens when a sample is a false positive (FP), for example, a healthy patient (null distribution) is diagnosed as diseased (alternative distribution).This is also called the probability of a type 1 error involving incorrectly rejecting the null hypothesis.However, as originally proposed, it applied to a theoretical distribution whereas the P value to experimental measurements. It has some analogy to a P value, and depends only on the null distribution. The value α is defined as the proportion of sample or measurements that are part of the null distribution that are incorrectly predicted to be members of the alternate distribution.We can however try to determine how good the metabolite is in predicting whether a patient is diseased, and a variety of statistics can be calculated. Of course due to overlapping distributions and lots of other factors such as diet, age, genetics, and also disease progression, which will influence the measured concentration of the metabolite, in most cases, the concentration of this potential marker will not perfectly separate samples into two groups. We may decide to diagnose patients as diseased if the measured concentration is more than 0.5 mg/mL. For example, the mean concentration of a metabolite in healthy (or control) patients might be 0.2 mg/mL and in diseased patients 0.9 mg/mL. This is the cut-off where samples are classified either as originating from the null or alternate distribution. Normally, a decision threshold is established. Once we set up an alternate hypothesis, there are many additional things we can calculate. Null and alternate hypotheses 2 DECISION THRESHOLD
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