Statistics with Computer Analysis Statistics Math 1551 Instructor Robert Barber

Use of Course Information This course material is intended solely for the use by the instructor and students enrolled in an approved course. This material is only for educational purposes and is not to be packaged and sold. Use of this material by others is not permitted without the express approval of this instructor. Credit is given to the authors of McClave and Sincich for their text, A First Course in Statistics (Ninth Edition), and Brase and Brase for their text, Understandable Statistics (Eighth Edition), and related materials upon which much of this presentation was based. Statistics Math 1552

Important Course Information All course information is on the MyClasses website, which can be reached at myclasses.salisbury.edu The website includes, syllabus, class policies, tentative class schedule, grades, and homework assignments The website also includes my office hours and office phone number and address. Statistics Math 1553

Major Course Requirements The statistical software package Mini-Tab will be used. Buy it for home use or find it on the computers in the school computer labs. A graphing calculator will be used for in- class tests, quizzes and exercises. The TI-83 or TI-84 is preferred because of extensive text reference. Statistics Math 1554

Keys to success Commit to excellence Attend and participate in class Seek help from me during my office hours Take advantage of free tutoring services Do your homework. Work other problems Ask questions about areas you do not understand. me at Read the textbook Get in a study group. Invite me sometimes. Statistics Math 1555

Course Objective To introduce the concepts of statistical inference by way of both non-parametric and classical parametric methods. Statistics Math 1556

What is statistics? Statistics is the science of collecting, classifying, organizing, describing, summarizing, analyzing, and interpreting numerical information for the purpose of making informed inferences about an unknown population(s) and to assist in the decision-making process regarding the population(s) of interest. Statistics Math 1557

Course Plan Step 1- Give you an understanding of the process of statistical analysis. Step 2- Relate the chapters in the textbook to the process and provide you with an understanding of why we are discussing each topic area. Step 3- Begin in chapter one and follow the sequence, i.e., the process, as we navigate through the text. Statistics Math 1558

Why do we do Statistics? A business wants to know if there is a market for a new product they developed. The government wants to know if it is safe to approve a new drug. You want to know which investment has the least risk. We want to predict the weather. Someone makes a claim and we want to test to see if the claim is believable. Statistics Math 1559

Statistics usually involves drawing a sample from a large population, analyzing the sample, and then drawing inferences about the overall population. Statistics Math 15510

Reasons for sampling! We cannot afford to measure the whole population. We may not be able to find the whole population even if we could measure it. We may not have the time to measure it all. Statistics Math 15511

Chapter 1 Statistics,Data, and Statistical Thinking What is the process for doing statistical analysis? What are the different types of data? How is data collected? What is the difference between a population and a sample ? What is the difference between descriptive and inferential data? Why is probability theory involved? Statistics Math 15512

Statistics Math STATISTICAL ANALYSIS PROCESS Population Sample Descriptive Statistics Probability Inferential Statistics ParametricNonparametric

Statistics Math STATISTICAL ANALYSIS PROCESS(Interfaces) Population Sample Descriptive Statistics Probability Inferential statistics ParametricNonparametric data statistics test results confidence intervals Reliability Measures

Statistics Math STATISTICAL ANALYSIS PROCESS(Chapters) Population Sample Descriptive Statistics Probability Inferential Statistics ParametricNonparametric Chapter 1 Chapter 2 Chapters 3&4 Chapters 5,6&7

Important Definitions Population- set of individuals, items, units of interest. Sample- a subset of individuals, items, units drawn from the population. Representative sample- a sample that fairly represents the diversity of the population and obtained through random sampling Statistics Math 15517

Definitions(continued) Experimental unit- the object in the population about which data is collected. Variable- a characteristic or property of the experimental unit

Important Definitions (continued) Descriptive Statistics- the processes of : ◦ using numerical and graphical methods to look for patterns in the collected data. ◦ determining summary measures which describe the data set for use in subsequent analysis. ◦ presenting data in a convenient understandable form. Statistics Math 15519

Important Definitions (continued) Inferential statistics- the processes used to make estimates, predictions, draw conclusions, or other generalizations about an unknown population(s) based on an analysis of the collected sample data. Statistical Inference- the estimate, prediction, conclusion, or other generalization made about a population(s). Statistics Math 15520

Food for thought! How much evidence is required to either accept or reject the claim of another? Statistics Math 15521

What is it that we measure? A characteristic of interest about each individual or object we measure. ◦ e.g., Height, color, GPA, temperature Statistics Math 15522

Types Of Data Data- the information collected or measured for each member of the sample. ◦ Qualitative data- information that cannot be found on a numeric scale, e.g., colors. ◦ Quantitative data- information that can be found on a numeric scale, e.g., heights. Statistics Math 15523

Measurement Scales (Levels of Measurement) Levels of Data Measurement ◦ Nominal- Categorical data. Data such as names, places, things. Mathematical operations are meaningless. ◦ Ordinal- Information that has a logical sequence or order. Data such as class rank, consumer opinions. Mathematical operations are meaningless. Statistics Math 15524

Measurement Scales (Levels of Measurement) (continued) ◦ Interval- numeric measured data where the interval between measurements is meaningful but division is not. e.g., Temperature. Data with no true zero. ◦ Ratio- measured numeric data where interval and ratios are meaningful. e.g., height. Data with a true zero. Statistics Math 15525

How is data obtained? Published documents, such as journals. Surveys, such as consumer questionnaires. Designed Experiments, such as tests on new medicines. Observational studies, such as observing and recording migration habits of birds. Statistics Math 15526

Difference Between Experiment and Observation Experiment- some treatment is imposed on some or all of the individuals. ◦ Some patients are given a drug while others are given a placebo. Observation- no treatment is imposed. ◦ Count the number of different colored cars in a parking lot. Statistics Math 15527

Another Form of Data Collection Simulation- a model or facimile of a real world phenomenon. Done when it is impractical to measure the real world. ◦ The effects of a nuclear blast. Statistics Math 15528

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Samples are reliable if: They are representative of the underlying population from which they are drawn, i.e., there are no selection bias errors. Measurement errors are minimized Care is taken when recording sample data Statistics Math 15530

How can you get a random sample? Use a Random Number Table. Use a Random Number Generator in MiniTab and the TI83/84. Statistics Math 15531

Different Sampling Techniques Stratified- items of interest are put into layers, e.g., seniors, juniors, etc. Systematic- every nth item is measured. Cluster- clusters a randomly picked and every item in a cluster is measured. Convenience- individuals are measured as they come along. Statistics Math 15532

Inferences are made in the context of a measure of reliability A measure of reliability is a statement about the degree of certainty or uncertainty associated with a statistical inference. Probability theory is a fundamental part of statistical analysis and the development of measures of reliability. Statistics Math 15533