Basic Issues in Statistics Kazeem Adepoju, PhD School of Statistics June 10, 2019 Outlines • Definition of Statistics • How Statistics Helps Us Learn about the World -Practical Questions -Its Importance, essentials and Procedure • How Inferences Are Made • Theory and Reality What is Statistics? • Statistics is the art and science of designing studies and analyzing the data that those studies produce. • Its ultimate goal is translating data into knowledge and understanding of the world around us. • In short, statistics is the art and science of learning from data . Practical Questions • How can you evaluate evidence about global warming? • Are cell phones dangerous to your health? • What’s the chance your tax return will be audited? • How likely are you to win the lottery? • Is there bias against women in appointing managers? • How can you analyze whether a diet really works? • How can you predict the selling price of a house? Importance • Making Conclusions in Medical Research Studies • Predicting an Election Using an Exit Poll • Consumers are sampled to provide information for predicting product preferences. • Using a Survey to Investigate People’s Beliefs Importance • controlled environmental conditions on humans in order to infer the appropriate treatment for various illnesses. • Engineers sample a product quality characteristic and various Decision Under Uncertainty • You’ll face financial decisions such as choosing between an investment with a sure return and one that could make you more money but could possibly cost you your entire investment. Statistics Essentials • You’ll learn how to analyze the available information to answer necessary questions in such scenarios. • Understanding of statistics is essential for making good decisions in an uncertain world Statistical Procedure • Statistical methods help us investigate questions in an objective manner. (1)formulate a statistical question (2)collect data (3) analyze data (4) interpret results How Inferences Are Made • Why is probability relevant to inferential statistics? Statistics are, in one sense, all about probabilities. Inferential statistics deal with establishing whether differences or associations exist between sets of data. The data comes from the sample we use, and the sample is taken from a population. How Inferences Are Made • Suppose that two candidates are running for a public office in our community and that we wish to determine whether our candidate, Jones, is favored to win. The population of interest is the set of responses from all eligible voters who will vote on election day, and we wish to determine whether the fraction favoring Jones exceeds .5. Elements of Science • 1. Reality: the real-world as it exists independently of human knowledge; • 2. Theory: coherent sets of ideas about how some portion of reality works; • 3. Data: observations and measurements on some real-world system; • 4. Models: abstract, but rigorous and specific, representations of reality, based on theory or data or both Theory and Reality • Theory: A collection of propositions to illustrate the principles of a subject. • In modern science, the term "theory" refers to scientific theories, a wellconfirmed type of explanation of nature, made in a way consistent with scientific method, and fulfilling the criteria required by modern science. • Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge. • Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter. Illustrative Example • For each of the following situations, identify the population of interest, the inferential objective, and how you might go about collecting a sample. (1) A university researcher wants to estimate the proportion of U.S. citizens from “Generation X” who are interested in starting their own businesses. Illustrative Example (2)A city engineer wants to estimate the average weekly water consumption for single-family dwelling units in the city. (3) A political scientist wants to determine whether a majority of adult residents of a state favor a unicameral legislature. NEXT • Descriptive and Inferential Statistics