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Looking at the above differences, it becomes clear as to why Test of Equivalence is considered as opposite of Hypothesis testing. Having laid down the differences, there are some similarities as well 1. Both work with samples and apply the concepts of Inferential Statistics (Significance Level, Confidence Intervals etc.) 2. Researcher is interested in Alternate Hypothesis in both (even though the alternate hypothesis are opposite in the two) Choice between hypothesis testing and equivalence will depend on the purpose of the study. Equivalence tests are most commonly used in pharma industry to check if a generic drug (lower cost option) has the same efficacy as the patented drug. To summarize, equivalence tests could be used wherever we want to use substitutes to an original item without significantly impacting the final outcome. Some e.g. that I could think off 1. Construction - Substituting building materials without impacting the compressive strength 2. Chemical / oil / pharma - Substituting chemicals without impacting the reaction time 3. Medical devices - substituting the type of laser without impacting the burning efficiency and precision 4. Tyre industry - substituting the rubber components without affecting the grip or the life of the tyre

Null hypothesis assumes that the population mean is the same as a target value or another population mean. In equivalence testing, the null hypothesis assumes the population mean differs from a target value or other population mean. For example, difference between a 2-sample t-test (Hypothesis) and a 2-sample equivalence test can be best illustrated as, 2-sample t-test to test whether the means of two populations are different. The hypotheses for the test are as follows: Null hypothesis (H0): The means of the two given populations are the same. Alternative hypothesis (H1): The means of the two given populations are different. If the p-value for the test is less than alpha (α), then the null hypothesis is rejected and concluded as the means are different. In contrast, 2-sample equivalence test is used to test whether the means of two populations are equivalent. Equivalence for the test is defined by a range of values that you specify (also called the equivalence interval). The hypotheses for the test are as follows: · Null hypothesis (H0): The difference between the means is outside equivalence interval. The means are not equivalent. · Alternative hypothesis (H1): The difference between the means is inside the equivalence interval. The means are equivalent. If the p-value for the test is less than α, then you reject the null hypothesis and conclude that the means are equivalent. Small differences between products are not always functionally or practically important. For example, a difference of 1 mg in a 200 mg dose of a drug is unlikely to have any practical effect. When an equivalence test is done we must enter equivalence limits that indicate how large the difference must be to be considered important. Smaller differences, which are within the equivalence limits, are considered unimportant. In this way, an equivalence test evaluates both the practical significance and statistical significance of a difference from the population mean. To choose between an equivalence test and a standard t-test, consider what needs to be proven or demonstrated. The objective of hypothesis test is to conclude the samples are different but when we want to prove that the samples are equivalent we use equivalence test. Equivalence testing is a better approach as compared to usual hypothesis testing when New food item meant to be a substitute New generic drug compared to old standard (bioequivalence) This process makes more sense logically because more samples gives us more power for detecting ‘equivalence’. An alternative to the two-sample t-test is TOST, designed specifically for bioequivalence testing of pharmaceutical products. It has recently been expanded into broader applications in pharmaceutical science, process engineering, psychology , medicine , chemistry and environmental science. An equivalence test forces us to identify from a practical perspective how big of a difference is important and puts the burden on the data to reach a conclusion of equivalence.

Bayes theorem is highly applicable in business scenarios wherever we want to find the probability of occurrence of any event when we have certain clues and guides regarding the processes impacting the outcome of happening of any event. Bayes theorem is closely associated with the Prior and Posterior probability in which the all the evidence and data associated with the occurrence of an event is well known in advance and that is primarily used to calculate the probability of occurrence of an event. One of the example associated with the manufacturing of textile machinery wherein the Bayes theorem applicability can be tested is: the consumption or procurement of the textile machinery are dependent on several factors. Lets say the most important factors among all those is the tax exemption announced by the Ministry of textiles for textile promotion. This is one of the probability with which the Original Equipment manufacturer can determine the probability of selling of the textile machinery. Thus Bayes theorem is associated with the degree of belief of a certain process to achieve certain specification. It can be accounted in two scenarios : Pre and Post gathering the evidence. once the probability is calculated before gathering the evidence it is called is Prior probability calculation and in case, probability is calculated after gathering the evidence, it is called posterior probability calculation.