Download Understanding Statistics: Definitions, Concepts, and Applications and more Assignments Statistics in PDF only on Docsity! What is Statistic? OPRE 6301 In today’s world. . . . . . we are constantly being bombarded with statistics and statistical information. For example: Customer Surveys Medical News Demographics Political Polls Economic Predictions Marketing Information Sales Forecasts Stock Market Projections Consumer Price Index Sports Statistics How can we make sense out of all this data? How do we differentiate valid from flawed claims? 1 Key Statistical Concepts. . . Population — a population is the group of all items of interest to a statistics practitioner. — frequently very large; sometimes infinite. E.g. All 5 million Florida voters (per Example 12.5). Sample — A sample is a set of data drawn from the population. — Potentially very large, but less than the population. E.g. a sample of 765 voters exit polled on election day. Parameter — A descriptive measure of a population. Statistic — A descriptive measure of a sample. 4 Pictorially, we have. . . Populations have Parameters, Samples have Statistics. Parameter Population Sample Statistic Subset 5 Descriptive Statistics. . . . . . are methods of organizing, summarizing, and present- ing data in a convenient and informative way. These methods include: Graphical Techniques (Chapter 2), and Numerical Techniques (Chapter 4). The actual method used depends on what information we would like to extract. Are we interested in. . . measure(s) of central location? and/or measure(s) of variability (dispersion)? Descriptive Statistics helps to answer these questions. . . 6 We use statistics to make inferences about parameters. Therefore, we can make an estimate, prediction, or deci- sion about a population based on sample data. Thus, we can apply what we know about a sample to the larger population from which it was drawn! Rationale: Large populations make investigating each member im- practical and expensive. Easier and cheaper to take a sample and make estimates about the population from the sample. However: Such conclusions and estimates are not always going to be correct. For this reason, we build into the statisti- cal inference “measures of reliability,” namely confi- dence level and significance level. 9 Confidence and Significance Levels. . . The confidence level is the proportion of times that an estimating procedure will be correct. E.g. a confidence level of 95% means that, estimates based on this form of statistical inference will be cor- rect 95% of the time. When the purpose of the statistical inference is to draw a conclusion about a population, the significance level measures how frequently the conclusion will be wrong in the long run. E.g. a 5% significance level means that, in the long run, this type of conclusion will be wrong 5% of the time. 10 If we use α (Greek letter “alpha”) to represent signifi- cance, then our confidence level is 1 − α. This relationship can also be stated as: Confidence Level + Significance Level = 1 Consider a statement from polling data you may hear about in the news: “This poll is considered accurate within 3.4 percentage points, 19 times out of 20.” In this case, our confidence level is 95% (19/20 = 0.95), while our significance level is 5%. 11
