Hypothesis testing is an important subject and step in all spheres of data analysis. The course aims at providing the basics of hypothesis testing with emphasis on some commonly encountered hypothesis tests in statistical data analysis such as in comparisons of averages, testing for variability, proportions and significance. This course will also introduce parametric and nonparametric test including simple and composite hypothesis. Various test methods are introduced for testing hypothesis of statistical data. This course will walk through the basics of statistical thinking and will teach the correct statistical tool to help answer our questions of interest.

Understand the fundamentals of hypothesis tests (examples might include one and two tailed hypotheses, types of errors, significance levels and p-values).

Be able to interpret an applied problem, selecting the correct hypothesis test.

Interpret mathematical models such as formulas, graphs, tables and schematics and draw inferences from them.

Today hypothesis testing constitutes the major foundation of data analysis. Through this course student will be able to

Validate parametric and non-parametric test for simple and composite hypothesis.

Use computers and the software package Excel, SPSS and R as a tool for data management and hypothesis testing.

Draw valid conclusions about hypotheses from the results of different statistical tests.

Justify conclusions even when no scientific theory exists.

Test of Significance: Basic concept, Idea of null and alternative hypotheses, Standard error, Test procedures, Probability value, Test of single proportion, mean and variance, Comparison of two and more proportions, means and variances, Test for correlation and regression coefficients, Test for independence and association of attributes in r x c contingency tables, Fisher’s exact test in 2 x 2 contingency table, Test for association in three-way contingency tables, Small sample tests of significance, Large sample tests.

Parametric Test: Basic concept, Simple and composite hypotheses, Errors in hypothesis testing, Critical region, Size of the test, Power, Best critical region (BCR), Power function, Power curve, Neyman-Pearson fundamental lemma, Most powerful critical region and test, Uniformly most powerful test, Two-sided BCR.

Non-parametric Test: Basic concept.  Sign, Run, Rank Sum, Randomization, Kolmogorov-Smirnov one and two samples, Kruskal-Wallis, Wilcoxon matched-pairs signed rank, Median, Mann-Whitney U, Rank correlation and goodness of fit tests.

Likelihood Ratio Test: Principles of likelihood ratio (LR) test, Distribution of LR statistic, Asymptotic distribution of LR statistic, Application of LR test, LR test in linear model.

Sequential Test: Introduction, SPRT, OC and ASN functions. Exercise on Binomial, Poisson, Normal and Exponential distributions.

Bayesian Hypothesis Testing: Introduction, Test of hypothesis concerning Normal and Exponential distributions in predictive approach.

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