© Copyright McGraw-Hill CHAPTER 1 The Nature of Probability and Statistics

© Copyright McGraw-Hill Objectives Demonstrate knowledge of statistical terms. Differentiate between the two branches of statistics. Identify types of data. Identify the measurement level for each variable.

© Copyright McGraw-Hill Objectives (cont’d.) Identify the four basic sampling techniques. Explain the difference between an observational and an experimental study. Explain how statistics can be used and misused. Explain the importance of computers and calculators in statistics.

© Copyright McGraw-Hill Introduction Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

© Copyright McGraw-Hill Descriptive and Inferential Statistics Descriptive statistics consists of the collection, organization, summarization, and presentation of data. Inferential statistics consists of generalizing from samples to populations, performing estimations hypothesis testing, determining relationships among variables, and making predictions.

© Copyright McGraw-Hill Basic Vocabulary Probability is the chance of an event occurring. A population consists of all subjects that are being studied. A sample is a group of subjects selected from a population.

© Copyright McGraw-Hill Variables and Data In order to gain knowledge about seemingly haphazard events, statisticians collect information for variables that describe the events. A variable is a characteristic or attribute that can assume different values. Data are the values that variables can assume.

© Copyright McGraw-Hill Variables and Data (cont’d.) A data set is a collection of data values. Each value in the data set is called a data value or a datum. Random variables have values that are determined by chance.

© Copyright McGraw-Hill Variables and Types of Data Qualitative variables can be placed into distinct categories according to some characteristic or attribute. Quantitative variables are numerical in nature and can be ordered or ranked.

© Copyright McGraw-Hill Variables and Types of Data (cont’d.) Quantitative variables can be further classified into two groups. Discrete variables assume values that can be counted. Continuous variables can assume all values between any two specific values.

© Copyright McGraw-Hill Levels of Measurement Nominal —classifies data into mutually exclusive (nonoverlapping), exhausting categories in which no order or ranking can be imposed on the data. Ordinal —classifies data into categories that can be ranked; however, precise differences between the ranks do not exist.

© Copyright McGraw-Hill Levels of Measurement (cont’d.) Interval —ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero. Ratio —possesses all the characteristics of interval measurement, and there exists a true zero.

© Copyright McGraw-Hill Classification of Data

© Copyright McGraw-Hill Data Collection and Sampling Techniques Surveys are the most common method of collecting data. Three methods of surveying are:  Telephone surveys  Mailed questionnaire surveys  Personal interviews

© Copyright McGraw-Hill Sampling Methods Random samples are selected using chance methods or random methods. Researchers obtain systematic samples by numbering each subject of the populations and then selecting every k th number.

© Copyright McGraw-Hill Sampling Methods Researchers select stratified samples by dividing the population into groups according to some characteristic that is important to the study, then sampling from each group. Researchers select cluster samples by using intact groups called clusters.

© Copyright McGraw-Hill Observational and Experimental Studies In an observational study, the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations. In an experimental study, the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.

© Copyright McGraw-Hill Uses and Misuses of Statistics Suspect samples  Very small samples  Bias sample selection  Volunteer samples Ambiguous averages Changing the subject

© Copyright McGraw-Hill Uses and Misuses of Statistics (cont’d) Detached statistics Implied connections Misleading graphs Faulty survey questions

© Copyright McGraw-Hill Computers and Calculators In the past, statistical calculations were done with pencil and paper. However, with the advent of calculators, numerical computations became easier.

© Copyright McGraw-Hill Statistical Packages Excel, MINITAB, and the TI-83 graphing calculator can be used to perform statistical computations. Students should realize that the computer and calculator merely give numerical answers and save time and effort of doing calculations by hand.

© Copyright McGraw-Hill Summary The two major areas of statistics are descriptive and inferential. When the populations to be studied are large, statisticians use subgroups called samples. The four basic methods for obtaining samples are: random, systematic, stratified, and cluster.

© Copyright McGraw-Hill Summary (cont’d.) Data can be classified as qualitative or quantitative. The four basic types of measurement are nominal, ordinal, interval, and ratio. The two basic types of statistical studies are observational and experimental.

© Copyright McGraw-Hill Conclusion The applications of statistics are many and varied. People encounter them in everyday life, such as in reading newspapers or magazines, listening to the radio, or watching television.