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What is Statistics?
McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 1
Dr. Ateq Ahmed Al-Ghamedi Department of Statistics P O Box 80203 King Abdulaziz University Jeddah 21589, Saudi Arabia [email protected]
GOALS
1. Understand why we study statistics.
2. Explain what is meant by descriptive statisticsand inferential statistics.
3 Distinguish between aqualitative variable
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3. Distinguish between a qualitative variable and a quantitative variable.
4. Describe how a discrete variable is different from a continuous variable.
5. Identify the four basic sampling techniques.
6. Explain the difference between an observational and an experimental study.
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What is Meant by Statistics?
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Statistics is the science of collecting, organizing, presenting,
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analyzing , and interpreting
numerical data to assist in making more effective decisions.
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What is Meant by Statistics?
zProbabilityis the chance of an event occurring.
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zProbabilitydeals more with creating models deals more with creating models and theoretical data while
and theoretical data while statisticsstatisticsdeals deals more with applying models and real data.
more with applying models and real data.
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Why Study Statistics?
1. Numerical information is everywhere
2. Statistical techniques are used to make decisions that affect our daily lives
3 The knowledge of statistical methods will help you
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3. The knowledge of statistical methods will help you understand how decisions are made and give you a better understanding of how they affect you.
No matter what line of work you select, you will find yourself faced with decisions where an understanding of data analysis is helpful.
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What is Meant by Statistics?
zIn the more common usage, statistics refers to numerical information
Examples: the average starting salary of college graduates, the
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number of deaths due to speeding last year, the change in the Tadawul Average from yesterday to today, and the number of home were stolen in Jeddah during the 2010 season.
zWe often present statistical information in a graphical form for capturing reader attention and to portray a large amount of information.
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Formal Definition of Statistics
Some examples of the need for data collection.
1 Research analysts for Merrill Lynch evaluate many facets of a STATISTICS The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.
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1. Research analysts for Merrill Lynch evaluate many facets of a particular stock before making a “buy” or “sell” recommendation.
2. The marketing department at P&G Co., a manufacturer of soap products, has the responsibility of making recommendations regarding the potential profitability of a newly developed group of face soaps having fruit smells.
3. The United States government is concerned with the present condition of the economy and with predicting future economic trends.
4. Managers must make decisions about the quality of their product or service.
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Who Uses Statistics?
Statistical techniques are used extensively by marketing, accounting quality control
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accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc...
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Types of Statistics – Descriptive Statistics and Inferential Statistics
Descriptive Statistics -methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 1:The United States government reports the population of the
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EXAMPLE 1: The United States government reports the population of the United States was 179,323,000 in 1960; 203,302,000 in 1970;
226,542,000 in 1980; 248,709,000 in 1990, and 265,000,000 in 2000.
EXAMPLE 2: According to the Bureau of Labor Statistics, the average hourly earnings of production workers was $17.90 for April 2008.
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Types of Statistics – Descriptive Statistics and Inferential Statistics
Inferential Statistics:A decision, estimate, prediction, or generalization about a population,based on a sample.
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Note: In statistics the word population andsample have a broader meaning. A population or sample may consist of individualsor objects
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Population versus Sample
A populationis a collection of allpossible individuals, objects, or measurements of interest.
Asample is a portion, or part, of the population of interest
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Population versus Sample
z A populationconsists of all subjects that are being studied.
z A sampleis a group of subjects selected from a population.
z Dataare the values that variables can assume.
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z Each value in the data set is called a data valueor a datum.
z A data setis a collection of data values.
z A variableis a characteristic or attribute that can assume different values.
z Random variableshave values that are determined by chance
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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
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3. Not possible to test or inspect all members of a population being studied
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Usefulness of a Sample in Learning about a Population
Using a sample to learn something about a population is done extensively in business, agriculture, politics, and government.
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EXAMPLE: Television networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers.
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Types of Variables
A. Qualitative or Attribute variable-the characteristic being studied is nonnumeric.
EXAMPLES:Gender, religious affiliation, type of automobile
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owned, state of birth, eye color are examples.
B. Quantitative variable- information is reported numerically.
EXAMPLES:balance in your checking account, minutes remaining in class, or number of children in a family.
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Quantitative Variables - Classifications
Quantitative variables can be classified as either discrete or continuous.
A. Discrete variables:can only assume certain values and there areusually “gaps”between values
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and there are usually gaps between values.
EXAMPLE:the number of bedrooms in a house, or the number of hammers sold at the local Store (1,2,3,…,etc).
B. Continuous variablecan assume any value within a specified range.
EXAMPLE:The pressure in a tire, the weight of a beef chop, or the height of students in a class.
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Summary of Types of Variables
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Four Levels of Measurement
Nominal level -data that is classified into categories and cannot be arranged in any particular order.
EXAMPLES:eye color, gender, religious affiliation
Interval level -similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.
EXAMPLE:Temperature on the Fahrenheit scale
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religious affiliation.
Ordinal level –data arranged in some order, but the differences between data values cannot be determined or are meaningless.
EXAMPLE:During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.
Fahrenheit scale.
Ratio level -the interval level with an inherent zero starting point.
Differences and ratios are meaningful for this level of measurement.
EXAMPLES:Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.
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Nominal-Level Data
Properties:
1. Observations of a qualitative variable can only be classifiedand counted.
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2. There is no particular order to the labels.
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Ordinal-Level Data
Properties:
1. Data classifications are represented by sets of labels or names (high, medium, low) that
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have relative values. 2. Because of the relative values,
the data classified can be ranked or ordered.
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Interval-Level Data
Properties:
1. Data classifications are ordered according to the amount of the characteristic they possess.
2. Equal differences in the characteristic are represented by
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equal differences in the measurements.
Example: Women’s dress sizes listed on the table.
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Ratio-Level Data
z Practically all quantitative data is recorded on the ratio level of measurement.
z Ratio level is the “highest” level of measurement.
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Properties:
1. Data classifications are orderedaccording to the amount of the characteristics they possess.
2. Equal differences in the characteristic are represented by equal differences in the numbers assigned to the classifications.
3. The zero point is the absence of the characteristic and the ratio between two numbers is meaningful.
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Why Know the Level of Measurement of a Data?
zThe level of measurement of the data dictates the calculations that can be done to summarize and present the data.
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zTo determine the statistical tests that should be performed on the data
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Summary of the Characteristics for Levels of Measurement
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Data Collection
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Data can be collected in a variety of ways. One of the most common ways is the use of surveys that can done by
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using a variety of methods. Three of the most common methods are:
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Telephone surveys
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Mailed questionnaire surveys
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Personal interviews
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Sampling Techniques
z Random samplesare selected using chance methods or random methods.
z Researchers obtain systematic samplesby numbering each subject of the populations and then selecting every n mber
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number.
z Researchers select stratified samplesby dividing the population into groups called strataaccording to some characteristic that is important to the study, then sampling from each group or strata.
z Researchers select cluster samplesby intact groups called clusters. Thus, dividing the population into groups and then taking samples of the groups
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Observational and Experimental Studies
¾ In an observational study, the researcher observes what is happening or what has
happened and tries to draw conclusions based on these observations.
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¾ In an experimental study, the researcher manipulates one of the variables and tries to determine how that influences other variables.
¾ In an experimental study, the subjects should be assigned to groups randomly. If this is not possible, then it is called a quasi-experimental
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Observational and Experimental Studies Statistical studies usually include one or more
independent variables and one dependent variable.
¾The independent variable or explanatory variableis the one that is being manipulated by the researcher
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the one that is being manipulated by the researcher.
¾The dependent variable or outcome variableis the resultant variable.
¾A confounding variableis the variable that influences the dependent variable but cannot be separated from the independent variable.
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Statistical Packages
zExcel, SPSS, MINITAB, SAS and the graphing calculator can be used to perform statistical computations.
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zStudents should realize that the computer and calculator merely give numerical answers and save time and effort of doing calculations by hand.
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Summary
z The two major areas of statistics are descriptiveand inferential. Inferential statistics is based on probability theory.
z Data can be classified as qualitativeor quantitative
z Quantitative data can be discreteor continuousdepending on the values they can assume.
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z Qualitative data can be nominalor ordinaldepending on the category they can assume.
z When the populationsto be studied are large, statisticians use subgroups called samples.
z The four basic methods for obtaining samples are: random, systematic, stratified, and cluster.
z The two basic types of statistical studies are observationaland experimental.
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