Chapter 1- Setting the Statistical Scene

Chapter 1- Setting the Statistical Scene

1. Introduction

   • Statistics as a set of mathematically based tools and techniques to transform raw (unprocessed) data in to a few summary measures that represent useful and usable information to support effective decision making
   • The statistical analysis in management decision making is performed via a Management decision support system which is illustrated in

2. The Language of Statistics

   • A number of important terms, concepts and symbols are used extensively in statistics
     • Random variable:
       • Any attribute of interest on which data is collected and analysed
     • Data:
       • The actual values (numbers) or outcomes recorded on a random variable
     • Information:
       • The results of data processing, and is meaningful
     • Sample:
       • A fraction or a subset of a population that is selected in order to carry out a survey. In many cases, researchers are compelled to use sample data instead of the full population
     • Sampling unit:
       • The object being measured, counted or observed with respect to the random variable under study
     • Sample statistic:
       • A measure that describes a characteristic of a sample
     • Population:
       • The collection of all possible data values that exist for the random variable under study
     • Population parameter:
       • A measure that describes a characteristic of a population

3. Components of Statistics

   • Descriptive statistics: condenses sample data into a few summary descriptive measures
     • When large quantities of data have been gathered, there is a need to organise, summarise and extract the essential information contained within this data for communication to management
     • These summary measures allow a user to identify profiles, patterns, relationships and trends within the data
   • Inferential statistics: generalises sample findings to the broader population
     • Descriptive statistics only describes the behaviour of a random variable in a sample
       • However, management is mainly concerned about the behaviour and characteristics of random variables in the population from which the sample was drawn
         • Inferential statistics is that area of statistics that allows managers to understand the population picture of a random variable based on the sample evidence
   • Statistical modelling: builds models of relationships between random variables
     • Constructs equations between variables that are related to each other
       • These equations (called models) are then used to estimate or predict values of one of these variables based on values of related variables

4. Statistical Applications in Management

   • Finance
     • At a company level, statistics is used to assess the validity of different investment projects
   • Marketing
     • analyse consumer behaviour, purchasing patterns, identifying viable market segments, determining media effectiveness
   • Human Resources
     • training, employee turnover, compensation planning, employee issues
   • Operations/ Logistics
     • machine utilisation, labour utilisation

5. Data and Data Quality

   • Data Quality
     • "Garbage in, garbage out"
     • Is influenced by four factors: datatype, data source, the method of data collection, data preparation
   • Selection of Statistical Method
     • Depends on management problem to be addressed and then on the type of data available

6. Data Types & Measurement Scales

   • Measurement Scales:
     • The scale determines the extent to which the data can be manipulated and also which statistical methods are appropriate to use on the data to produce valid statistical results
       • Nominal data
         • is associated with categorical data. If all the categories of a qualitative random variable are of equal importance, then this categorical data is termed ‘nominal-scaled’
         • gender (1 = male; 2 = female)
         • city of residence (1 = PTA; 2 = DBN)
       • Ordinal data
         • is also associated with categorical data, but has an implied ranking between the different categories of the qualitative random variable
         • Each consecutive category possesses either more or less than the previous category of a given characteristic
         • size of clothing (1 = small; 2 = medium)
         • product usage level (1 = light; 2 = moderate; 3 = heavy)
       • Interval data
         • Interval data is associated with numeric data and quantitative random variables
         • It is generated mainly from rating scales, which are used in survey questionnaires to measure respondents’ attitudes
       • Ratio data
         • Ratio data consists of all real numbers associated with quantitative random variables
         • employee ages (years), customer income (R), distance travelled (km)
         • Ratio data has all the properties of numbers (order, distance and an absolute origin of zero) that allow such data to be manipulated using all arithmetic operations
   • Data Types
     • Qualitative random variables
       • Generate categorical (non-numeric) response data. The data is represented by categories only
         • gender of a consumer
         • an employee’s highest qualification
     • Quantitative random variables
       • Generate numeric response data. These are real numbers that can be manipulated using arithmetic operations (add, subtract, multiply and divide)
         • age of an employee
         • machine downtime
         • price of a product in different stores
     • Discrete data: is whole number (or integer) data
       • no. of students in a class, no of cars sold
     • Continuous data: is any number that can occur in an interval
       • the time needed for an assembly line, the volume of fuel for a car

7. Data Sources

   • Classification
     • internal
       • financial reports; departmental records or reports
     • external
       • internet; media
   • Primary data is data that is recorded for the first time at source and with a specific purpose in mind
     • advantage of primary-sourced data is its high quality
     • disadvantage of primary-sourced data is that it can be time consuming and expensive to collect
   • Secondary data is data that already exists in a processed format
     • advantages. First, its access time is relatively short (especially if the data is accessible through the internet), and second it is generally less expensive
     • disadvantages are that the data may not be problem specific (i.e. problem of its relevancy), it may be out of date

8. Data Collection Methods

   • Observation
     • Primary data can be collected by observing a respondent or a process in action
     • Advantage: the respondent is unaware of being observed and therefore behaves more naturally or spontaneously
     • Disadvantage: the passive form of data collection. There is no opportunity to probe for reasons or to further investigate underlying causes
   • Surveys
     • The direct questioning of respondents using questionnaires to structure and record the data collection
     • Advantages: a higher response rate is generally achieved. it allows probing for reasons. the data is current and generally more accurate
     • Disadvantages: personal interviews are: time consuming. expensive to conduct
   • Telephone interviews
     • Advantages: cost is relatively low. questions can be clarified by the interviewer
     • Disadvantage: loss of respondent anonymity
   • Experimentation
     • the analyst manipulates certain variables under controlled conditions
     • Advantage: high quality
     • Disadvantage costly and time-consuming
   • E-survey
     • Is geographically dispersed and it is not practical to conduct personal interviews
     • Advantages: Interviewer bias is eliminated. anonymity of each respondent is assured
     • Disadvantage: low response rates

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