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STATISTICS FOR BUSINESS 903182
DR. MAHMOUD OMAR AL-TABARI
American University of Madaba Faculty of Business & Finance
Faculty of Science
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The Where, Why, and Howof Data Collection
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Learning Outcomes
Outcome 1. Know the key data collection methods.
Outcome 2. Know the difference between a population and a sample.
Outcome 3. Understand the similarities and differences between different
sampling methods.
Outcome 4. Understand how to categorize data by type and level of
measurement.
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Why we study Statistics?
• To learn about the most useful business procedures available for decision makers.
• To learn how to transform data into information effectively.
“Statistical thinking will one day be as necessary for efficient citizenship as the
ability to read and write” HG Wells
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1.1 What is Business Statistics?
Statistics
Plural Form“Numerical Data”
Is a collection of facts placed in relation to each other, affected by
variety of causes, numerically expressed, enumerated or
estimated and collected in a systematic manner for a pre-
determined purpose.
Singular Form“Statistical Methods” or
“Statistical Science”Is the science of collecting, organizing, presenting, analyzing, and interpreting
numerical data to assist in making more effective decisions.
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1.1 What is Business Statistics?
• The field of Statistics is a branch of applied mathematics, it collect and interprets data, then uses probability theory to draw potential conclusions. In short, statistics is the math behind the data.
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1.1 What is Business Statistics?
• A collection of procedures and techniques used to convert data into meaningful information in a business environment
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Statistical Procedures (Division of Statistics)
• Descriptive Statistics– Procedures and techniques designed to
describe data• Inferential Statistics
– Tools and techniques that help decision makers to draw inferences from a set of data
• Mathematical Statistics• Applied Statistics• Inductive Statistics• Analytical Statistics
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Descriptive Procedures
• Descriptive Statistics: Comprises the statistical methods dealing with the collection, organization, presentation and summarization of data, so as to present meaningful information. Examples:– Organization of data in tabulated form (frequency distribution)
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With Against No decision Total
30 15 5 50
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Descriptive Procedures
• Descriptive Statistics: Examples (continue):– Pictorial representation of data (charts,
graphs, histogram,…)
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With Against No decision0
5
10
15
20
25
30
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Descriptive Procedures
• Descriptive Statistics: Examples (continue):– Computing numerical measurements for data
characteristics (mean or average, standard deviation)
– “60% of these students agree with switching to electronic exam system, 30% against it while 10% has no decision”
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1 Sum of all data valuesAverage
Number of data values
N
ii
x
N
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Inferential Procedures
• Inferential Statistics: Consists of the methods involved with the analysis and interpretation of data collected from only a small part (sample) of a larger dataset (population), that will used to develop meaningful inferences about the large dataset (population).
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Inferential Procedures
• Estimation– e.g., Estimate the population mean weight
using the sample mean weight
• Hypothesis Testing– e.g., Use sample evidence to test the claim
that the population mean weight is 120 pounds
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1.2 Procedures for Collecting Data
Types of DataPrimary DataIs the data collected by a
particular organization from its own recourses for its
own use.
Secondary Data
Is the data collected, organized, presented, and may be described by some
organization for its own use, and then published it
in order to be used by other organizations.
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1.2 Procedures for Collecting Data
Data Collection Techniques
Written questionnaires and
surveys
Experiments
Telephone surveys
Direct observation and personal
interview
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Experiments
• Experiment – A process that produces a single outcome
whose result cannot be predicted with certainty.
• Experimental design – A plan for performing an experiment in which
the variable of interest is defined.
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Telephone Surveys
• Closed-End Questions– Questions that require the respondent
to select from a short list of defined choices
• Demographic Questions – Questions relating to the respondents’
characteristics, backgrounds, and attributes
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Major Steps for aTelephone Survey
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Written Questionnaires
• Similar to telephone surveys• Closed-end and open-end questions• Open-End Questions
– Questions that allow respondents the freedom to respond with any value, words, or statements of their own choosing.
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Major Steps for a WrittenQuestionnaires Survey
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Observations and Interviews
• Direct Observations– Data are being collected is physically observed
and the data recorded based on what takes place in the process.
– Subjective and time-consuming• Personal Interviews
– Structured: questions are scripted– Unstructured: begin with one or more broadly
stated questions, with further questions being based on the responses
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Data Collection Techniques
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Data Collection Issues
• Main Steps for Survey:1) Define the purpose and the objectives of the
study very carefully
2) Determine the method of collecting the data (e.g., phone, email, face to face interview, questioner)
3) Define the population of interest
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Data Collection Issues
• Main Steps for Survey (continue):4) Design the Survey Instruments:
A. Make questions clear and unmistakable
B. Use universally-accepted definitions
C. Limit the number of questions
5) Present the Survey Instruments:A. Pilot test with a small group of participants
B. Assess clarity and length
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Data Collection Issues
• Main Steps for Survey (continue):6) Determine the sample size and sampling
method
7) Select sample and administer the survey
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Data Collection Issues
• Survey Recommendations– Use closed-end questions (questions that
require the respondent to select from a short list of defined choices)
– Avoid open-end questions as you can (it makes the responses difficult to analyze)
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Data Collection Issues
• Survey Requirements– The survey instrument should contain
demographic questions (e.g., gender, income level, educational level) which allow you to:
• Break down responses• Look deeper into the survey result
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Data Collection Issues
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Interviewer Bias
Nonresponsive Bias
Selection Bias
Observer Bias
Measurement Error
Internal Validity
External Validity
Data Accuracy
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1.3 Populations, Samples, and Sampling Techniques
• Population– The set of all objects or individuals of interest
or the measurements obtained from all objects or individuals of interest
• Sample– A subset of the population
• Census– An enumeration of the entire set of
measurements taken from the whole population
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Population vs. Sample
Population Sample
“Is the largest collection of entities
(people, objects, transactions, events, etc.) for which we have an interest at particular time”
“Is a subset of the population”
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Population vs. Sample
a b c d
e f g h i j k l m n
o p q r s t u v
w x y z
Population Sample
b c
g h k l m n
o r s v
w z
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Population
Types of PopulationFinite
“It has entities thatcan be counted from a first
to a last Element”
Infinite“It has entities
that cannot be counted (there is no
last element in the population)”
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Parameters and Statistics
• Parameters– Descriptive numerical measures, such as an
average or a proportion, that are computed from an entire population
• Statistics– Corresponding measures computed for a sample
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Parameters and Statistics
• Very often we can not perform a complete survey of the population– the population is infinite or dynamic– the population is finite, but sufficiently large– some aspect of a population that "destroys”
the entities– the population is undergoing rapid change
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Sampling Techniques
• Probability or Statistical Sampling– Sampling methods that use selection techniques
based on chance selection• Non-Probability or Non-Statistical Sampling
– Methods of selecting samples that use convenience, judgment, or other non-chance processes.
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Sampling Techniques
Convenience
Sampling Techniques
Nonstatistical Sampling
Judgment
Statistical Sampling
Simple Random
Systematic
Stratified Cluster
Ratio
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Nonstatistical Sampling
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• Convenience– Collected in the most convenient manner for
the researcher• Judgment
– Based on judgments about who in the population would be most likely to provide the needed information
• Ratio
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Nonstatistical Sampling
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• Used when:– it is impossible to use statistical sampling
methods– lake of an adequate population frame– low frequency of entities in the population with
the characteristic of interest• Should be avoided in any scientific research,
since these methods are almost guaranteed to introduce bias into any study and no correct inference could be drawn from such sample
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Nonstatistical Sampling
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• In case of using non-statistical sampling:– The researcher can only summarizes the
data, present it graphically or in a tabulation form and describe it
– No further analysis can be done– Any conclusions drawn from such sampling
methods will be applicable only to that particular set of entities used in the study
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Statistical Sampling
• Items of the sample are chosen based on known or calculable probabilities
Statistical Sampling(Probability Sampling)
SystematicStratified ClusterSimple Random
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Statistical Sampling
• Also called probability sampling• Allows every item in the population to
have a known or calculable chance of being included in the sample– simple random sampling– stratified random sampling – systematic sampling– cluster sampling
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Simple Random Sampling
• Used in case that the population is homogeneous
• Every possible sample of a given size has an equal chance of being selected
• Selection may be with replacement or without replacement
• The sample can be obtained using a table of random numbers or computer random number generator
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Stratified Random Sampling• Used for heterogeneous population regarding some
characteristics• Divide population into subgroups (called strata) according
to some common characteristic– e.g., gender, income level
• Select a simple random sample from each subgroup• Combine samples from subgroups into one
Populationdividedinto 4strata
Sample
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Stratified Sampling Example
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• Decide on sample size: n• Divide ordered (e.g., alphabetical) frame of N
individuals into groups of k individuals: k = N / n• Randomly select one individual from the 1st
group • Select every kth individual thereafter
Systematic Random Sampling
N = 64
n = 8
k = 8
First Group
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• Systematic sampling yields a probability sample but it is not a random sampling strategy
• Systematic sampling is faster and easier to take than simple random sampling in cases where the frame consists of a listing of pre-numbered entities
Systematic Random Sampling
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Cluster Sampling• A sampling technique that overcomes the geographical
spread problem is cluster sampling• Divide population into several “clusters,” each
representative of the population (e.g., county)• Select a simple random sample of clusters
– All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique
Population divided into16 clusters.
Randomly selected clusters for sample
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Sampling and Non-sampling errors
• Sampling error is inherent in the method of sampling and refers to the heterogeneity or chance differences from sample to sample. Sampling error:– can be measured and controlled– can be reduced by increasing the sample size and following an
efficient sampling techniques
• Non-sampling error are automatically occurred due to human error and independent on the sampling methods. Non Sampling error:– are unpredictable (can not be measured) and not easily controlled– may increase with increases in sample size
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1.4 Data Types and Data Measurement Levels
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• Data is the raw material of statistics• The term "Raw data" refers to numbers in its original form
before any statistical techniques are applied to redefine; process or summarize it
Generation of Data in statistics
CountingProcess
MeasurementProcess
Numbers
Data
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1.4 Data Types and Data Measurement Levels
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• Numbers result from Measurement Process: For example when we measure the height of a person, a number such as 170 cm. might be obtained
• Numbers result from Counting Process: For example when we count the number of smoking persons in a certain group of people, a number such as 20 men might be obtained.
• Variable: A variable is a characteristics or attribute that can assume different values for different entities. Examples: height of adult males, weight of preschool children, number of floors in buildings, graduation grade, marital status
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1.4 Data Types and Data Measurement Levels
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Data Types
• Quantitative: – measurements whose values are inherently
numerical• discrete (e.g. number of children)• continuous (e.g. weight, volume)
• Qualitative: – data whose measurement scale is inherently
categorical (e.g. marital status, political affiliation, eye color)
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Data Types
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Types of Variables
Quantitative variables
Their values convey information
regarding the amount of the characteristics they
represent.These variables are
measured bythe usual way of measurement.
(Decimals, Integers)
Qualitative Variables
Their values convey information
regarding the attribute they represent. These variables
are measured by categorization. They called also categorized variables.
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Data Types
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Variables classified according to their effect on other variables as:
Independent variables
“is that variable who has an effect on another variable in
some certain circumstances”
(e.g., Supply, Demand, Import,
Export, Income Distribution)
Dependent variables
“is that variable who is affected by one or more other variable in some certain circumstances”
(e.g., Price)
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Data Timing
• Time-Series: – a set of consecutive data values observed at
successive points in time (e.g. stock price on daily basis for a year)
• Cross-Sectional: – A set of data values observed at a fixed point
in time (e.g. bank data about its loan customers)
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Data Timing
Data classified according to considering variation in times as:
Time Series Data or Longitudinal Data“Refers to data collected by
following one subject's changes over a different
equally spaced point in time (years, months, days)”.For time series, we are interested in trends and
patterns over time.
Cross Sectional Data
“Refers to data collected by observing many subjects (such
as individuals, firms or countries/regions) at the same point of time, or without regard
to differences in time”.It’s analysis is usually consists of comparing the differences
among the subjects or in relationships between
variables.
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Data Timing Example
• Examples of Cross Sectional Data:– GPA of students in a statistics class– Traffic fatalities in the biggest 10 cities
• Examples of Time Series Data:– National income (GDP, consumption,
investment)– Economic indicators (Consumer Price Index,
unemployment rate etc.)
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Data Timing Example
Sales (in $1000s)
2009 2010 2011 2012
Atlanta 435 460 475 490
Boston 320 345 375 395
Cleveland 405 390 410 395
Denver 260 270 285 280
Time Series Data
Cross Sectional Data
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Data Measurement Levels
• Scales of measurement refer to ways in which variables/numbers are defined and categorized
• Each scale of measurement has certain properties which in turn determines the appropriateness for use of certain statistical analyses
• The four scales of measurement are:– Nominal level of measurement– Ordinal level of measurement– Interval level of measurement– Ratio level of measurement
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Data Measurement Levels
Nominal Level of Measurement• This is the lowest level of measurement.• Assigning codes to categories generates nominal data.• According to it, the values a variable can take is classified into
mutually exclusive (non-over-lapping) and exhausting (contain all values of the variable) categories in which no order or ranking can be imposed on these values.
• Examples:– Marital status (1. Single, 2. Married, 3. Divorced, 4. Widowed, 5. Abandoned).– Class subject in collage of business administration: (1. Management, 2. Accounting,
3. Statistics, 4. Mathematics, 5. Systems, 6. Computer).– Gender (1. Male, 2. Female).
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Data Measurement Levels
Ordinal Level of Measurement• This is the next higher level of measurement.• The values a variable can take are classified into mutually exclusive and
exhausting categories in which order or ranking can be imposed on these values.
• This level of measurement has an advantage over the nominal scale of measurement; this advantage is the ability to rank different categories. Nevertheless, we can not measure the difference between these categories.
• Examples:– Educational level (1. Preliminary, 2. High school, 3. Diploma, 4. Collage degree, 5. Master degree,
6. Doctorate degree).– Health condition for new patient received by a hospital: (1. Critical, 2. Serious, 3. Moderate, 4.
Minor)– Ranks of competing individuals in a contest, represents ordinal data.
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Data Measurement Levels
Interval Level of Measurement• This level of measurements is higher than the ordinal level.
• According to the interval scale, the values a variable can take are naturally ranked and precise differences between these values exist (because this scale has equal units), but comparisons between them have no meaning. This is because the absence of true zero.
• Examples:– Temperature on Fahrenheit or Celsius scales. – Scores of a psychological tests: For example, intelligent quotation score, IQ score.– Measurement of Sea Level, represents ordinal data.
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Data Measurement Levels
Ratio Level of Measurement• This is the highest level of measurements.
• It possesses all the characteristics of interval level of measurement besides the existence of a true (absolute) zero, (as which zero means “none”), i.e. with the ability of comparisons between different values.
• Examples:– Height of adult females.– Time spend to complete certain task.– Family income.
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Data Measurement Levels
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Data Measurement Levels
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Categorizing Data
• Identify each factor in the data set• Determine whether the data are time-
series or cross-sectional• Determine which factors are quantitative
data and which are qualitative data• Determine the level of data measurement
for each factor.
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Data Categorization Example
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Qualitative, nominal-level data Quantitative, interval, ratio-level data
Cross-sectional data
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Summery
• In this Chapter we have learned about many of the terms associated with the use of statistics, procedures for collecting data, population, sampling, sampling techniques, data, and variables in statistics.
• You should be comfortable with all of the terms and concepts before proceeding to the next chapter.
• Each new chapter builds upon the concepts and ideas discussed in previous chapter, so make sure you are comfortable with what you have been presented with so far before you continue on to the next chapter.
• In the coming chapter we will discuses procedures for Describing data visually (Graphs, charts, and Tables).