Topic 1 The Nature Of Probability And Statistics 3b6l23

Elementary Statistics 1-1

A Step by Step Approach Sixth Edition

by Allan G. Bluman SLIDES PREPARED BY LLOYD R. JAISINGH MOREHEAD STATE UNIVERSITY MOREHEAD KY © The McGraw-Hill Companies, Inc., 2000

1-2

Topic 1 Chapter One: The Nature of Probability and Statistics

WCB/McGraw-Hill

© The McGraw-Hill Companies, Inc., 1998

1-3

Outline  

 

1-1 Introduction 1-2 Descriptive and Inferential Statistics 1-3 Variables and Types of Data 1-4 Data Collection and Sampling Techniques © The McGraw-Hill Companies, Inc., 2000

1-4

Outline 

1-5 Observational and experimental studies

© The McGraw-Hill Companies, Inc., 2000

1-5

Objectives 





Demonstrate knowledge of all statistical . Differentiate between the two branches of statistics. Identify types of data.

© The McGraw-Hill Companies, Inc., 2000

1-6

Objectives 



Identify the measurement level for each variable. Identify the four basic sampling techniques.

© The McGraw-Hill Companies, Inc., 2000

1-7

Objectives 

Explain the importance of computers and calculators in statistics.

© The McGraw-Hill Companies, Inc., 2000

1-8

1-1 Introduction 

Statistics consists of conducting studies to collect, organize, summarize, analyze, and draw conclusions.

© The McGraw-Hill Companies, Inc., 2000

1-9

1-2 Descriptive and Inferential Statistics 



Data are the values (measurements or observations) that the variables can assume. Variables whose values are determined by chance are called random variables. © The McGraw-Hill Companies, Inc., 2000

1-10

1-2 Descriptive and Inferential Statistics 



A collection of data values forms a data set. Each value in the data set is called a data value or a datum.

© The McGraw-Hill Companies, Inc., 2000

1-11

1-2 Descriptive and Inferential Statistics 

Descriptive statistics consists of the collection, organization, summation, and presentation of data.

© The McGraw-Hill Companies, Inc., 2000

1-2 Descriptive and Inferential Statistics

1-12





A population consists of all subjects (human or otherwise) that are being studied. A sample is a subgroup of the population.

© The McGraw-Hill Companies, Inc., 2000

1-2 Descriptive and Inferential Statistics

1-13



Inferential statistics consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions. © The McGraw-Hill Companies, Inc., 2000

1-14

Example: Attendance & Grades 

A study conducted at Manatee Community College revealed that students who attended class 95% to 100% of the time usually received an A in the class. Students who attended class 80% to 90% of the time usually received a B or C in the class. Students who attended class less than 80% of the time usually received a D or an F or eventually withdrew from the class. © The McGraw-Hill Companies, Inc., 2000

1-15

Example: Attendance & Grades Answer the following questions: 1. What are the variable under study? 2. What are the data in the study? 3. Are descriptive, inferential, or both types of statistics used? 4. What is the population under study? 5. Was a sample collected? If so, from where? 6. From the information given, comment on the relationship between the variables. © The McGraw-Hill Companies, Inc., 2000

1-16

1-3 Variables and Types of Data 

Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. For example, gender (male or female).

© The McGraw-Hill Companies, Inc., 2000

1-17

1-3 Variables and Types of Data 

Quantitative variables are numerical in nature and can be ordered or ranked. Example: age is numerical and the values can be ranked.

© The McGraw-Hill Companies, Inc., 2000

1-18

1-3 Variables and Types of Data 



Discrete variables assume values that can be counted. Continuous variables can assume all values between any two specific values. They are obtained by measuring. © The McGraw-Hill Companies, Inc., 2000

1-19

Classification of Variables Data

Qualitative

Quantitative

Discrete

Continuous

© The McGraw-Hill Companies, Inc., 2000

1-20

1-3 Variables and Types of Data 

The nominal level of measurement classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data. © The McGraw-Hill Companies, Inc., 2000

1-21

1-3 Variables and Types of Data 

The ordinal level of measurement classifies data into categories that can be ranked; precise differences between the ranks do not exist.

© The McGraw-Hill Companies, Inc., 2000

1-22

1-3 Variables and Types of Data 

The interval level of measurement ranks data; precise differences between units of measure do exist; there is no meaningful zero.

© The McGraw-Hill Companies, Inc., 2000

1-23

1-3 Variables and Types of Data 

The ratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist for the same variable.

© The McGraw-Hill Companies, Inc., 2000

1-24

Examples of Measurement Scale Nominal

Ordinal

Interval

Ratio

Zip code

Grade

Exam score

Height

Gender

Rating scale

IQ exam

Weight

Eye color

Ranking of tennis players

Temperature

Age

Nationality

Salary

Major field © The McGraw-Hill Companies, Inc., 2000

1-25

Example: Transportation Safety The chart shows the number of job-related injuries for each of the transportation industries for 1998.

Industry Railroad Intercity bus Subway Trucking Airline

Number of Injuries 4520 5100 6850 7144 9950 © The McGraw-Hill Companies, Inc., 2000

1-26

Example: Transportation Safety Answer the following questions: 1. What are the variable under study? 2. Categorize each variable as quantitative or qualitative. 3. Categorize each quantitative variable as discrete or continuous. 4. Identify the level of measurement for each variable. © The McGraw-Hill Companies, Inc., 2000

1-4 Data Collection and Sampling Techniques

1-27  





Data can be collected in a variety of ways. One of the most common methods is through the use of surveys. Surveys can be done by using a variety of methods Examples are telephone, mail questionnaires, personal interviews, surveying records and direct observations. © The McGraw-Hill Companies, Inc., 2000

1-4 Data Collection and Sampling Techniques

1-28





To obtain samples that are unbiased, statisticians use four methods of sampling. Random samples are selected by using chance methods or random numbers. © The McGraw-Hill Companies, Inc., 2000

1-29

Example 

A lottery draw is a good example of simple random sampling. A sample of 6 numbers is randomly generated from a population of 45, with each number having an equal chance of being selected.

© The McGraw-Hill Companies, Inc., 2000

1-4 Data Collection and Sampling Techniques

1-30



Systematic samples are obtained by numbering each value in the population and then selecting the kth value.

© The McGraw-Hill Companies, Inc., 2000

1-31

Example 





If a systematic sample of 500 students were to be carried out in a university with an enrolled population of 10,000, the sampling interval would be: I = N/n = 10,000/500 =20 All students would be assigned sequential numbers. The starting point would be chosen by selecting a random number between 1 and 20. If this number was 9, then the 9th student on the list of students would be selected along with every following 20th student. The sample of students would be those corresponding to student numbers 9, 29, 49, 69, ........ 9929, 9949, 9969 and 9989. © The McGraw-Hill Companies, Inc., 2000

1-4 Data Collection and Sampling Techniques

1-32



Stratified samples are selected by dividing the population into groups (strata) according to some characteristic and then taking samples from each group.

© The McGraw-Hill Companies, Inc., 2000

1-33

Example 

The committee of a company of 1,000 employees wishes to assess any reaction to the reintroduction of security system into the company. To ensure a representative sample of employees from all departments, the committee uses the stratified sampling technique. In this case the strata are the departments. Within each strata the committee selects a sample. So, in a sample of 100 employees, all departments would be included. The employees in the sample would be selected using simple random sampling or systematic sampling within each strata © The McGraw-Hill Companies, Inc., 2000

1-4 Data Collection and Sampling Techniques

1-34



Cluster samples are selected by dividing the population into groups and then taking samples of the groups.

© The McGraw-Hill Companies, Inc., 2000

1-35

Example 

Suppose an organization wishes to find out which lung cancer treatment doctors are recommending in across Malaysia. It would be too costly and take too long to survey every doctor, or even some doctors from every hospital. Instead, 100 hospitals are randomly selected from all over Malaysia. These hospitals are considered to be clusters. Then, every doctor in these 100 hospitals is surveyed. In effect, doctors in the sample of 100 hospitals represent all doctors in Malaysia. © The McGraw-Hill Companies, Inc., 2000

1-36

Cluster vs. Stratified 

Cluster sampling is different from stratified random sampling, because in the latter sampling technique, some units are selected from each group.

© The McGraw-Hill Companies, Inc., 2000

1-37

1-5 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.

© The McGraw-Hill Companies, Inc., 2000

1-38

1-5 Observational and Experimental Studies 

In an experimental study, the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.

© The McGraw-Hill Companies, Inc., 2000

1-39

1-5 Observational and Experimental Studies 



The independent variable (explanatory variable) in an experimental study is the one that is being manipulated by the researcher. The resultant variable is called the dependent variable (outcome variable). © The McGraw-Hill Companies, Inc., 2000

1-40

1-5 Observational and Experimental Studies 

A confounding variable is one that influences the dependent or outcome variable but cannot be separated from the independent variable.

© The McGraw-Hill Companies, Inc., 2000

1-41

Example: Observational or Experimental Study? (a) Subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. After 6 months, the numbers of respiratory tract infections each group had were compared. Experimental Study © The McGraw-Hill Companies, Inc., 2000

1-42

Example: Observational or Experimental Study? (b) A researcher stood at a busy intersection to see if the color of the automobile that a person drives is related to running red lights.

Observational Study © The McGraw-Hill Companies, Inc., 2000

1-43

Example: Observational or Experimental Study? (c) A researcher finds that people who are more hostile have higher total cholesterol levels than those who are less hostile.

Observational Study © The McGraw-Hill Companies, Inc., 2000

1-44

Example: Observational or Experimental Study? (d) Subjects are randomly assigned to four groups. Each group is placed on one of four special diets – a low-fat diet, a highfish diet, a combination of low-fat diet and high-fish diet, and a regular diet. After 6 months, the blood pressures of the groups are compared to see if diet has any effect on blood pressure. Experimental Study

© The McGraw-Hill Companies, Inc., 2000