A Unified Approach to Testing Hypotheses About Parameters of a Normal Population (original) (raw)

Tests of Hypotheses Using Statistics

We present the various methods of hypothesis testing that one typically encounters in a mathematical statistics course. The focus will be on conditions for using each test, the hypothesis tested by each test, and the appropriate (and inappropriate) ways of using each test. We conclude by summarizing the different tests (what conditions must be met to use them, what the test statistic is, and what the critical region is).

A Note on Testing of Hypothesis

In this paper problem of testing of hypothesis is discussed when the samples have been drawn from normal distribution. The study of hypothesis testing is also extended to Baye’s set up.

Chapter 6: Statistical Methods

How should data be analyzed and patterns identified? Are the bulk of the data of greatest interest or are the fewer, rarer, possibly outlying, values most informative in answering relevant questions? How should outliers be handled? How well suited for handling small data sets are statistical hypothesis tests? These are questions that robust statistical theorists attempt to answer.

Clear-Sighted Statistics: Module 15: Hypothesis Tests (slides)

2020

Distinguish between independent & dependent samples Conduct a z-test for two independent means Conduct a z-test for two independent proportions Conduct a F-test for equality of variance Conduct a t-test for the means assuming equal variance 1 Clear-Sighted Statistics Lecture Objectives (continued) Conduct a t-test for the means assuming unequal variance Conduct a t-test for the means of two dependent samples Measure Effect Size Estimate the probability of a Type II Error & statistical power 2 2 Clear-Sighted Statistics

APPLICATIONS AND LIMITATIONS OF PARAMETRIC TESTS IN HYPOTHESIS TESTING

The process of testing research hypothesis is important for researchers, academicians, statisticians, policy implementers among other users. It enables concerned individuals to deduce meaning as well as make decisions based on the outcomes of the tests (accepting or rejection of null hypothesis). A research hypothesis has been defined by statisticians who have also advanced various ways of testing a research hypothesis using statistical tests. The tests of hypothesis (tests of significance) include the parametric and non-parametric tests. The parametric tests are based on the assumption that the samples are drawn from a normal population and on interval scale measurement whereas non-parametric tests are based on nominal as well as ordinal data and it requires more observations than parametric tests. However, in this essay paper the parametric tests will be the centre of focus. In parametric tests, the common ones involves Normal (Z) tests, Student (t) tests, Fischer’s (F) tests, regression analysis, correlation analysis and the Chi-square (ᵡ2) test.

HYPOTHESIS TESTING

CCDRC , 2023

Hypothesis testing is the foundation for statistical analysis. This paper gives you a deeper understanding about the concept.

On the Third Edition of Testing Statistical Hypotheses

Selected Works of E. L. Lehmann, 2011

In this article, the history of the third edition of Testing Statistical Hypotheses will be discussed. Sometime during the fall of 1998, Erich Lehmann and Julie Shaffer visited the Statistics Department at Stanford during one of our Tuesday joint colloquia with the Berkeley Statistics Department. While having coffee prior to the seminar, Erich asked me if we could have a quick chat. During this seemingly impromptu conversation, Erich asked if I would be willing to work on the revision of his testing book. Coming from a man I so truly admire, I was genuinely taken aback by this offer. After all, Erich's testing book was rightly regarded as one of the most important books in statistics, and it has had an enormous and enduring impact since the first edition appeared in 1959. Overwhelmed by the offer, I told Erich I would soon get back to him. My immediate thoughts were that this was an extraordinary opportunity for me to work with Erich on the book, but it also was an enormous responsibility to live up to the high standard of excellence that the first and second editions already held. There was also the matter that I was already working on a book on subsampling with Dimitris Politis and Michael Wolf, and I never imagined I would undertake another book project, at least not so soon. Over the years at Stanford, I had taught estimation and testing from Erich's texts. But, I wondered why Erich chose to ask me to work on this project. As a student at Berkeley, I took Erich's first-year graduate sequence, Statistics 210, with Javier Rojo and Dorota Dabrowska as the teaching assistants for the course that year. I was quite proud that I got perfect scores on all six exams which I took from Erich during my first year at Berkeley. But after graduating in 1986, I had not had much contact with Erich,