chapter 1 (2)

Copyright ©2014 Pearson Education, Inc.

STATISTICS FOR BUSINESS 903182

DR. MAHMOUD OMAR AL-TABARI

American University of Madaba Faculty of Business & Finance

Faculty of Science

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Copyright ©2014 Pearson Education, Inc. 1-2

The Where, Why, and Howof Data Collection


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.


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


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.



• 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.



• A collection of procedures and techniques used to convert data into meaningful information in a business environment


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



• 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

35



• 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


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).


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


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.


1.2 Procedures for Collecting Data

Data Collection Techniques

Written questionnaires and

surveys

Experiments

Telephone surveys

Direct observation and personal

interview


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


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


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


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



• 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



• Main Steps for Survey (continue):6) Determine the sample size and sampling

method

7) Select sample and administer the survey



• 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)



• 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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Interviewer Bias

Nonresponsive Bias

Selection Bias

Observer Bias

Measurement Error

Internal Validity

External Validity

Data Accuracy


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”


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


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)”


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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• 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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• 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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• 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



• Items of the sample are chosen based on known or calculable probabilities

Statistical Sampling(Probability Sampling)

SystematicStratified ClusterSimple Random



• 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


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


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


• 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


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


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


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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• 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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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.


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)


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.


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


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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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).



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.



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.



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.


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


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).

chapter 1 (2)

Documents

pearson education

business statistics

organization of data

data characteristics

summarization of data

interpretation of data

field of statistics

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