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.