![]() Using the other null hypothesis, a type 1 error would mean that the system would have to be changed (this is costly!) and that the state would receive fewer income from taxes. In this case, a type 1 error means that the taxation system doesn’t have to be changed. In this case, assuming that the new system leads to less income from taxation, that is, \(H_0: A \geq B\) is clearly the better option (if you are optimizing with regard to tax income). You don’t introduce the simplified approach and miss out on additional taxation income. Incorrectly conclude that the old system was better. So, after changing to the simplified taxation system, you realize that you actually acquire fewer taxes. Incorrectly conclude that the new system leads to greater income. ![]() Let A be the amount of tax income with the old, complicated system and let B be the income with the new, simplified system. The government thinks about simplifying the taxation system. Thus, albeit actually superior to A, B is never released and resources have been wasted.Įvidently, having \(H_0: A \geq B\) is the more appropriate null hypothesis because its type 1 error is more detrimental (lives are endangered) than that of the other null hypothesis (patients do not receive access to a better drug). You falsely conclude that drug A is superior to drug B. Thus, you introduce B to the market, thereby risking the life of patients where B was favored over A. You falsely conclude that drug B is superior to drug A. However, given effectivity measures A and B for the old and the new drug, respectively, how should the null hypothesis be formulated? Take a look at the consequences of the Here, you definitely want to use a directional test in order to show that one drug is superior over the other. Having developed a new drug, your company wants to decide whether it should supplant the old drug with the new drug. Let’s assume there’s a well-tried, FDA-approved drug that is effective against cancer. For example, power is determined more readily available for parametric than for non-parametric tests. ![]() Note that it depends on the test whether it’s possible to determine the statistical power. Experiments are often designed for a power of 80% using power analysis. Traditionally, the type 1 error rate is limited using a significance level of 5%. The test itself: some tests have greater power than others for a given data set.Significance level: power increases with increasing significance levels.Sample size: power increases with increasing number of samples.Effect size: power increases with increasing effect sizes.The power of a test depends on the following factors: The power answers the following question: If there is an effect, what is the likelihood of detecting it? Thus, power is a measure of sensitivity.The significance level answers the following question: If there is no effect, what is the likelihood of falsely detecting an effect? Thus, significance is a measure of specificity.The power of a statistical test is defined by \(1 - \beta\). Type 1 and type 2 error rates are denoted by \(\alpha\) and \(\beta\), respectively. Type 1 and type 2 errors are defined in the following way for a null hypothesis \(H_0\): Decision/Truth
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