CHAPTER14: INTRODUCTION TO DATA ANALYSIS

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CHAPTER14INTRODUCTION TO DATA ANALYSIS
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14.1 INTRODUCTION

• There are many situations in business where data
  is collected and analysed.
• The key ideas of data analysis are important in
  the modern business environment.
• Summarising and understanding the main features
  of the variables contained within the data, and
  investigate the nature of any linkages between
  the variables that may exist.

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14.2 WHAT IS DATA

• Example 1
• Population the set of all people/objects of
  interest in the study being undertaken.
• Very large
• Enumerated precisely
• Cannot be Enumerated physically

Population member
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• The information for each member of the
  population
• Age
• Gender
• Parish
• Will you vote in the by-election?
• Will you vote for me?
• Variables one piece of information
• Five variables

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• To investigate the connection between the two
  pairs of variables
• 'Will you vote for me' and 'Age'
• 'Will you vote for me' and 'Gender'
• 'Will you vote for me' and 'Parish'
• Population data is used ? the outcomes of the
  analysis are precise ? 'perfect information'
  results.

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• Example 2

• Population the set of all customers

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• A sensible initial set of questions is
• Do you understand exactly what each variable is
  measuring/recording?
• Do you understand the problem under investigation
  and are the objectives of the investigation
  clear.?

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14.3 DESCRIBING VARIABLES

• Classification of variable types
• Attribute variables
• Measured variables

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• Attribute Variables
• An attribute variable has its outcomes described
  in terms of its characteristics or attributes.
• Example 1 'By-Election Data'

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• Example 2 'Credit Data'
• Does the customer own their own house?
• 0Yes 1No
• The Region in which the customer is resident?
• 1South West
• 2South East
• 3London
• 4Midland
• 5North
• Handling attribute data is to give it a
  numerical code 0, 1, 2 ,.

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• Measured Variable
• A measured variable is a variable that has its
  outcomes measured the resulting outcome is
  expressed in numerical terms.
• Two types of measured variables
• Continuous variable continuous scale of
  measurement(person's weight)
• Discrete variable the number of passengers on
  flight
• Example 1 'By-Election Data'
• The measured variable in this data set is 'Age'

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• Example 2 'Credit Data'
• Measured variables as follows

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14.4 THE CONCEPT OF A STATISTICAL DISTRIBUTION

• Attribute Variable
• Gender of constituents (Example 1)

DISTRIBUTION OF GENDER IN THE CONSTITUENCY
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• REGION (Example 2)

DISTRIBUTION OF REGION IN WHICH CUSTOMER IS
RESIDENT
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• Measured Variable
• Customer's Age (Example 2)

DISTRIBUTION OF AGE OF CUSTOMER
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• Household Income (Example 2)

DISTRIBUTION OF HOUSEHOLD INCOME
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• What does the distribution show?
• The area under the curve from one income value to
  another measures the relative proportion of the
  population having household incomes in that
  range.
• Lower than 10,000 is relatively rare
• Large proportion of the population have Household
  incomes between 20,000 50,000

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• The Descriptive Statistics for Distribution of a
  Measured Variable
• Distribution of the height of adults in Great
  Britain.

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• The height of children under 11 years of age

children's heights
adult's heights


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• Heights in two different countries, country A
  and country B

DISTRIBUTION OF HEIGHTS COUNTRY A B
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• A statistical distribution for a measured
  variable can be summarised using three key
  descriptions
• Centre of the distribution
• Width of the distribution
• Symmetry of the distribution

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• Measuring the Centre of a Distribution
• The Mean
• average value ?X/n
• Average Household Income
• symbol for the population mean ?
• Formally the population mean of a variable is
  defined to be
• ? ?X/n
• The Median
• The median value of the variable is defined to be
  the particular value of the variable such that
  half the data values are less than the median
  value and half are greater.
• Sorting all data in ascending order, the median
  value is then the middle value in this list

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• Measuring the Width of a Distribution
• The Standard Deviation
• The Standard Deviation is the square root of the
  average squared deviation from the mean.
• Symbol of Standard Deviation ?
• ? is usually defined in terms of the variance ?
  2as
• ? 2 ?(X- ?)2/n
• Standard deviation is the square root of the
  variance
• Calculating the standard deviation for the
  variable Household Income
• Standard deviation is a relative measure of
  spread (width), the larger the standard deviation
  the wider the distribution.

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• Inter-quartile Range
• The inter-quartile range is the range over which
  the middle 50 of the data values varies
• To define the quartiles
• Q1 the value of the variable that divides the
  distribution 25 to the left and 75 to the
  right.
• Q2 the value of the variable that divides the
  distribution 50 to the left and 50 to the
  right.
• Q3 the value of the variable that divides the
  distribution 75 to the left and 25 to the
  right.
• The inter-quartile range is the value Q3 - Q1

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• Calculating the Q1, Q2, Q3 for the variable
  'Household Income'
• Conventionally the mean and standard deviation
  are one pair of measures of location and spread,
  and the median and inter-quartile range as
  another pair of measures.

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• Measuring the Symmetry (skewness) of a
  Distribution
• Pearson's coefficient of Skewness
• Pearson's coefficient of Skewness 3(mean -
  median)/standard deviation
• Quartile Measure of Skewness
• Quartile Measure of Skewness (Q1 - Q3) - (Q2
  Q1)/(Q3 Q1)

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14.5 SUMMARY

• What is Data
• Variables
• Two types of variable
• an attribute variable
• a measured variable
• The concept of a Statistical Distribution
• As applied to an attribute variable
• As applied to a measured variable

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• Descriptive Statistics for a measured variable
• Measures of Centre
• Mean
• Median
• Measures of Width
• Standard Deviation
• Inter-Quartile Range
• Measures of Symmetry (Skewness)
• Pearson's coefficient of Skewness
• Quartile Measure of Skewness

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14.6 THE NATURE OF A SAMPLE

• POPULATION
• Perfect Information
• In practice it is often impossible to enumerate
  the whole population.
• A sample drawn from the population to make
  judgements (inferences) about the population.

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• SAMPLE
• Imperfect Information
• Random sample
• Each item in the population has an equal chance
  of being included in the sample.
• The KEY PROBLEM is to use this sample data to
  draw valid conclusions about the population with
  the knowledge of and taking into account the
  'error due to sampling'
• Unrepresentative sample
• How to Lie with Statistics

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• A Credit Scenario
• Population the set of all customers who used the
  credit facilities between 1st January 2000 and
  31st December 2001.
• Sample Size 654 customers
• Data file BDMCREDIT.MTW

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14.8 DESCRIBING SAMPLE DATA

• Attribute variable the number of occurrences of
  each attribute is obtained
• Measured variable Sample descriptive statistics
  describing the centre, width and symmetry of the
  distribution are calculated.

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• Attribute Data
• C5 Does the customer own their own house? Coded
  0 Yes, lNo
• C6 The Region in which the customer is
  resident? Coded
• 1                     South West
• 2                     South East
• 3                     London
• 4                     Midlands
• 5                     North
• Command STAT-TABLE-TALLY

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• Summary Statistics for Discrete Variables
• Counts (OWN-OCC)
• Percent(OWN-OCC)
• Distribution graph(OWN-OCC)

Do you Own your own house?
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• Summary Statistics for Discrete Variables
• Count(REGION )
• The information in form
• 74 or 11.31 of the respondents are from the
  Southwest
• 132 or 20.18 of the respondents are from the
  Southeast
• 165 or 25.23 of the respondents are from the
  London area
• 161 or 24.62 of the respondents are from the
  Midlands
• 122 or 18.65 of the respondents are from the
  North

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• Measured Variables
• For the 'Credit Data
• C2 Customer's Age (AGE)
• C3 Household Income ( per annum) (SALARY)
• C4 Estimated monthly outgoing on
  mortgage/rent/rates/utilities/credit card
  payments etc. (PAYOUT)
• C7 The Amount borrowed on credit (CREDIT)
• HISTOGRAM

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• BOXPLOT
• The BOXPLOT will prove to be a more useful way of
  representing the picture of a sample distribution
  when the data analysis used to examine the
  connection between two sample variables is
  discussed in later chapters.

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14.7 DATA ANALYSIS USING SAMPLE DATA

• Before attempting to analyse any data, the
  analyst should
• The problem under investigation is clearly
  understood and the objectives of the
  investigation have been clearly specified. Keep
  asking questions until satisfactory answers have
  been obtained.
• The individual variables making up the dataset
  are clearly understood.

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• Descriptive Statistics
• Measures of Centre
• Mean
• Sample Mean
• Median
• Measures of Width
• Standard Deviation
• Sample Standard Deviation S
• Sample Variance S2
• Inter-Quartile Range IQR
• Symmetry

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• Symmetry (Skewness)
• A distribution is skewed if one tail extends
  farther than the other.
• A value close to 0 indicates symmetric data.
• Negative values indicate negative/left skew.
• Positive values indicate positive/right skew.
• Example of a negative or left-skewed distribution
  (skewness -1.44096)

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• The Relationship between the descriptive
  statistics and the Boxplot
• The asterisks on the right hand side of the
  median are indicating sample values that are in
  some sense extreme

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14.9 INVESTIGATING RELATIONSHIPS BETWEEN
VARIABLES

• To investigate the relationship between
  variables.
• Response variable
• a variable that measures either directly or
  indirectly the objectives of the analysis
• Explanatory variable
• a variable that may influence the response
  variable

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• Example 1
• A university wishes to investigate the salary of
  its graduates five years after graduating
• The questionnaire
• 'Current Salary'
• 'Starting Salary'
• 'Class of Degree' Coded lFirst, 2Upper
  Second, 3Lower Second, 4Third, 5Pass.
• 'Graduate's Gender' Coded lMale, 2Female.
• Response variable
• Current Salary (measured variable)

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• Explanatory Variable
• Staring Salary (measured variable)
• Class of Degree (attribute variable)
• 'Graduate's Gender (attribute variable)

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• Example 2 CREDIT scenario
• Objectives of the analysis
• To investigate the nature of credit transactions
• The variable 'The Amount borrowed on credit'
• The problem is to investigate the relationship
  between 'The Amount borrowed on credit' and the
  other variables.
• Summary

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• Combinations of Response Variable and
  Explanatory Variable

EXPLANATORY VARIABLE
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• The method for investigating the connection
  between a response variable and an attribute
  variable depends on the type of variable.
• Investigating the connection between a measured
  response and a measured explanatory variables
• Investigating the connection between a measured
  response and an attribute explanatory variables

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Homework

• Find or collect some data in your life or
  business practice, answer the following questions
• Draw the statistic distribution of data
• Calculate the Mean and Standard Deviation
• Calculate the Median and Inter-Quartile Range
• Calculate the Pearsons Coefficient of Skewness
  and Quartile Measure of Skewness