Download - Lecture 1
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• Statistics is the science of data collection, organising and interpreting numerical facts.
• Gaining information from numerical data or making sense of data.
• Descriptive Statistics – Organising and summarising data – condense large
volumes of data into a few summary measures.
• Statistical inference – Generalises subset data findings to the broader
universe.
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• Statistical analysis in management decision-making
Input Process Output
Data Statistical
Analysis Information
Decision
Making
Raw
Observations
Transformation
Process
Useful,
Usable
Meaningful
MANAGEMENT DECISION SUPPORT SYSTEM
→
→
→ → → →
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PLANNING
DATA
COLLECTION
CONCLUSIONS
DECISION-
MAKING
• Approach for the Statistical process
ANALYSIS
EDITING
and CODING
Primary and
secondary
sources
Descriptive Statistics
Statistical inference
Research process
becoming a cycle
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• Basic concepts of Statistics – Parameter
• Computed from the universe.
– Statistic • Computed from the subset taken from the universe.
– Variable
• Characteristic of the item being observed or measured.
– Data
• Collection of observations on one or more variable.
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• Basic concepts of Statistics – Population
• Entire group we want information about.
– Sample
• The proportion of the population we actually examine.
• Representative and not biased.
• Random sampling.
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• Basic concepts of Statistics – Census
• Investigate the whole population
• Expensive
• Time consuming
• Sections of population is inaccessible
• Units are destroyed
• Inaccurate
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• Sampling methods – Probability sampling
• Each element has a known probability of being
selected as part of sample.
• Unbiased inference about the population.
– Non-probability sampling • Element from the population are not selected
random.
• The elements are selected without knowing the
probability of being selected as part of sample.
• We can not use results of these samples to make
conclusions about the population.
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• Sampling methods – Probability sampling
– Simple random sampling • Number the elements of the population from
1 to N.
• Select a random starting point in the random table.
• From the starting point read systematically in any direction.
• Divide the digits in the random table into groups with the same number of digits as the number of digits in the population size (N).
• Find n random numbers from 1 to N – no duplicates.
• Identify each of the chosen random numbers in the population.
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• Sampling methods – Probability sampling
– Stratified random sampling
• Population heterogeneous with respect to the variable
under study.
• Population divided into
homogeneous sub-
populations called strata.
• Sample size form each
sample proportional to
stratum size.
• Draw a simple random sample
from each of the stratum.
N = N1 + N2 + ….. + Nk
(k = number of stratum)
n = n1 + n2 + ….. + nk
(k = number of stratum)
, 1...ii
Nn n i k
N
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• Sampling methods – Non-probability sampling
– Convenience sampling
• Not representative of the target population.
• Items being selected because they are easy to find,
inexpensive and self selected.
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• Sampling methods – Non-probability sampling
– Quota sampling
• Population divided into sub-classes according to a
certain characteristic.
• A non-sampling method is used to select a sample
from each stratum.
• It is a technique of convenience.
• Researcher attempts to fill the quota quickly.
• Sample is not representative of the population.
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• Sampling methods – Non-probability sampling
– Judgement sampling
• Elements from the population are chosen by the
judgement of the researcher.
• The probability that an element will be chosen cannot
be calculated.
• Sample is biased.
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• Sampling methods – Non-probability sampling
– Snowball sampling
• Is used where sampling units are difficult to locate
and identify.
• Find a person who fits the profile of characteristics
of the study.
• From this person obtain names and locations of
others who will fit the profile.
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Discrete
(integer)
Continuous
(any numerical value)
DIFFERENT
TYPES OF
DATA
QUANTITATIVE
(numerical scale)
QUALITATIVE
(categorical)
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DIFFERENT
TYPES OF
DATA
Interval
scaled
Ratio
scaled
QUANTITATIVE
(numerical scale)
QUALITATIVE
(categorical)
Nominal
scaled Ordinal
scaled
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• Problems associated with the collection
of data:
– Characteristics have to be measured.
– Measurements can be complicated.
– Measurements must be valid and accurate.
– Secondary data not easy to validate.
– Data can be incomplete, typographical errors,
small sample.
– Biased or misleading responses.
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• Problems associated with the collection
of data:
– Make sure of the following:
• Who conducted the study?
• What data was collected?
• What sampling method was used?
• Sample size?
• Chance of bias?
• Is data relevant to the problem at hand?
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• How to design a questionnaire
– Questions should: • Be simply stated.
• Have no suggestion of a specific answer.
• Be specific and address only one issue.
• Carefully word sensitive issues.
• Not require calculations or a study to be answered.
– Types of questions: • Closed
• Open
• Combined
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• Appearance and layout of a questionnaire – Attractive look.
– Coloured paper.
– Clear instructions on how to complete.
– Reasonably short.
– Enough space to complete questions.
– Mother-tongue language.
– Interesting questions first.
– Simple questions first, controversial questions later.
– Complete one topic before starting the next.
– Important information first.
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• Interview
– Fieldworker completed questionnaire
• Higher response rate and data collection is immediate.
– Mailed questionnaires
• When population is large or dispersed.
• Low response rate.
• Time consuming.
– Telephone interview
• Lower costs.
• Quicker contact with geographically dispersed
respondents.
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• Editing the data
– Obvious errors should be eliminated.
– Eliminate questionnaires that are incomplete
and unreliable.
– Questionnaires should be pre-tested on a small
group of people.