济南大学泉城学院毕业论文外文资料翻译Statistical hypothesis testingLast updated 44 minutes agoAdriana Albu，Loredana UngureanuPolitehnica University Timisoara, adrianaaaut.utt.roPolitehnica University Timisoara, loredanauaut.utt.roAbstract In this article, we present a Bayesian statistical hypothesis testing inspection, testing theory and the process Mentioned hypothesis testing in the real world and the importance of, and successful test of the Notes.Key words Bayesian hypothesis testing; Bayesian inference; Test of significanceIntroduction A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study (not controlled). In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. The phrase test of significance was coined by Ronald Fisher: Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first.1Hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory data analysis. In frequency probability, these decisions are almost always made using null-hypothesis tests. These are tests that answer the question Assuming that the null hypothesis is true, what is the probability of observing a value for the test statistic that is at least as extreme as the value that was actually observed?) 2 More formally, they represent answers to the question, posed before undertaking an experiment, of what outcomes of the experiment would lead to rejection of the null hypothesis for a pre-specified probability of an incorrect rejection. One use of hypothesis testing is deciding whether experimental results contain enough information to cast doubt on conventional wisdom.Statistical hypothesis testing is a key technique of frequentist statistical inference. The Bayesian approach to hypothesis testing is to base rejection of the hypothesis on the posterior probability.34 Other approaches to reaching a decision based on data are available via decision theory and optimal decisions.The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis. The critical region is usually denoted by the letter C.One-sample tests are appropriate when a sample is being compared to the population from a hypothesis. The population characteristics are known from theory or are calculated from the population.Two-sample tests are appropriate for comparing two samples, typically experimental and control samples from a scientifically controlled experiment.Paired tests are appropriate for comparing two samples where it is impossible to control important variables. Rather than comparing two sets, members are paired between samples so the difference between the members becomes the sample. Typically the mean of the differences is then compared to zero.Z-tests are appropriate for comparing means under stringent conditions regarding normality and a known standard deviation.T-tests are appropriate for comparing means under relaxed conditions (less is assumed).Tests of proportions are analogous to tests of means (the 50% proportion).Chi-squared tests use the same calculations and the same probability distribution for different applications: Chi-squared tests for variance are used to determine whether a normal population has a specified variance. The null hypothesis is that it does. Chi-squared tests of independence are used for deciding whether two variables are associated or are independent. The variables are categorical rather than numeric. It can be used to decide whether left-handedness is correlated with libertarian politics (or not). The null hypothesis is that the variables are independent. The numbers used in the calculation are the observed and expected frequencies of occurrence (from contingency tables). Chi-squared goodness of fit tests are used to determine the adequacy of curves fit to data. The null hypothesis is that the curve fit is adequate. It is common to determine curve shapes to minimize the mean square error, so it is appropriate that the goodness-of-fit calculation sums the squared errors. F-tests (analysis of variance, ANOVA) are commonly used when deciding whether groupings of data by category are meaningful. If the variance of test scores of the left-handed in a class is much smaller than the variance of the whole class, then it may be useful to study lefties as a group. The null hypothesis is that two variances are the same - so the proposed grouping is not meaningful.The testing processIn the statistical literature, statistical hypothesis testing plays a fundamental role. The usual line of reasoning is as follows:1. There is an initi