Chapter 1 Introduction To Statistics PDF

Chapter 1 Introduction to Statistics  Learning Objective ◼ Introduction to the field of statistics ◼ How statistics applies to real-world problems ◼ Establish the link between statistics and data ◼ Differentiate between population and sample data ◼ Differentiate between desc...

Chapter 1 Introduction to Statistics  Learning Objective ◼ Introduction to the field of statistics ◼ How statistics applies to real-world problems ◼ Establish the link between statistics and data ◼ Differentiate between population and sample data ◼ Differentiate between descriptive and inferential statistics 2  What is Statistics? ◼ Statistics is the science of data. – observations (such as measurements, genders, survey responses) that have been collected 3  What is Statistics? Statistics The science of collecting, organizing, analyzing, and interpreting data in order to make decisions. 4  What is Data? Data Consist of information coming from observations, counts, measurements, or responses. “People who eat three daily servings of whole grains have been shown to reduce their risk of stroke by 37%.” (Source: Whole Grains Council) “Seventy percent of the 1500 U.S. spinal cord injuries to minors result from vehicle accidents, and 68 percent were not wearing a seatbelt.” (Source: UPI) 5  Data Sets Population The collection of all outcomes, responses, measurements, or counts that are of interest. Sample A subset of the population. 6 Why take a sample instead of studying every member of the population? 1. Prohibitive cost of census 2. Destruction of item being studied may be required 3. Not possible to test or inspect all members of a population being studied 7  Example: Identifying Data Sets In a recent survey, 1708 adults in the United States were asked if they think global warming is a problem that requires immediate government action. Nine hundred thirty-nine of the adults said yes. Identify the population and the sample. Describe the data set. (Adapted from: Pew Research Center) 8  Solution: Identifying Data Sets The population consists of the responses of all adults in the U.S. Responses of adults in The sample consists of the the U.S. (population) responses of the 1708 adults in Responses of the U.S. in the survey. adults in survey (sample) The sample is a subset of the responses of all adults in the U.S. The data set consists of 939 yes’s and 769 no’s. 9  Parameter and Statistic Parameter A number that describes a population characteristic. Average age of all people in the United States Statistic A number that describes a sample characteristic. Average age of people from a sample of three states 10  Example: Distinguish Parameter and Statistic Decide whether the numerical value describes a population parameter or a sample statistic. 1. A recent survey of a sample of MBAs reported that the average salary for an MBA is more than $82,000. (Source: The Wall Street Journal) Solution: Sample statistic (the average of $82,000 is based on a subset of the population) 11  Example: Distinguish Parameter and Statistic Decide whether the numerical value describes a population parameter or a sample statistic. 2. Starting salaries for the 667 MBA graduates from the University of Chicago Graduate School of Business increased 8.5% from the previous year. Solution: Population parameter (the percent increase of 8.5% is based on all 667 graduates’ starting salaries) 12 Types of Statistical Applications Statistics Descriptive Inferential Statistics Statistics 13  Types of Statistical Applications Descriptive Statistics Inferential Statistics Involves organizing, Involves using sample summarizing, and data to draw displaying data. conclusions about a population. e.g. Tables, charts, averages 14  Types of Statistical Applications Descriptive statistics utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set and to present that information in a convenient form. Average, spread, range, frequency, histogram, median, 15 Types of Statistical Applications Inferential statistics utilizes sample data to make estimates, decisions, predictions or other generalizations about a larger set of data. Hypothesis test, z. ANOVA, confidence interval, ordinary 16  Fundamental Elements of Statistics Descriptive Statistics Inferential Statistics The population or sample of Population of interest interest One or more variables to be One or more variables to be investigated investigated The sample of population units Tables, graphs or numerical summary tools The inference about the population based on the Identification of patterns in sample data the data A measure of reliability of the inference 17  Example: Descriptive and Inferential Statistics Decide which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics? A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65. (Source: The Journal of Family Issues) 18  Solution: Descriptive and Inferential Statistics Descriptive statistics involves statements such as “For unmarried men, approximately 70% were alive at age 65” and “For married men, 90% were alive at 65.” A possible inference drawn from the study is that being married is associated with a longer life for men. 19 The Steps in Inferential Statistics Define the objective of the experiment and the population of interest Determine the design of the experiment and the sampling plan to be used Collect and analyze the data Make inferences about the population from information in the sample Determine the goodness or reliability of the inference. 20  Uses of Statistics Statistics is a theoretical discipline in its own right Statistics is a tool for researchers in other fields Used to draw general conclusions in a large variety of applications 21  Learn to View Statistics with a Critical Eye There are three kinds of lies….. – Lies – Damned Lies – Statistics You need to make statistics work for you, not lie for you! ✓ Emphasis should be on importance of using statistics responsibly and ethically. ✓ It is a tool for understanding data, making informed decisions rather than misrepresenting information for personal gain. 22