Dr Henry Bailey, ECON 1005 Statistics lecture notes

1. ECON 1005 Lecture #1
An Introduction to Statistics
(based largely on PS Mann Chapter 1)
Dr. Henry Bailey
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2. About this course
• Lecture Sessions
• Tutorial Sessions
• Assessment
– Final exam
– Coursework (On-line)
• Resources on myelearning
• Recommended Text
• Study methods
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3. • Statistics is the science of collecting, analyzing,
presenting, and interpreting data, as well as of
making decisions based on such analyses.
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4. • Statistics is the science of collecting, analyzing,
presenting, and interpreting data, as well as of
making decisions based on such analyses.
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5. The word “Statistics” is used in two ways:
• Numbers or ‘numerical facts:
• a discipline or field of study:
“Statistics” has been
around for a long time:
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6. Every day we have to make decisions.
• These decisions are often made under conditions of
uncertainty, with no precise or definite solution (shall I
take an umbrella with me today?)
• Statistical methods help us to make scientific and
intelligent decisions in such situations (is the sky grey?
Does a grey sky usually herald rain? What does the
weather forecast say, and is it usually correct?)
• Decisions made using statistical methods are
“educated guesses”
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7. • It influences nearly all facets of our society.
• It offers some methods for making sense out of numbers.
• It makes real the fact that society need not (and cannot) be run purely on
the basis of hunches, or trial and error. Increasingly, numbers have
become the basis of rational decisions instead of hunches in government,
business, sports, and politics to name a few.
• Experience has established that many aspects of social progress depend
on the correct analysis of numerical data.
• Decisions based on sound data are proving to give better results to
decision-makers.
• The advent of the computer and available information and communication
technologies (ICT) have led to an unprecedented ‘data explosion’ in which
we are subjected to a barrage of economic figures and claims about
product superiority. 8

8. • “my grandmother smoked 50 cigarettes
every day and lived to 105 years old;
therefore smoking cannot be bad for you !”
• Notice the attempt here to draw a conclusion from
one observation.
• In Statistics, we say that there is statistical evidence
to show that people are more likely to die young if
they smoke heavily than if they do not.
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9. Like many fields of study, Statistics has two aspects:
theoretical and applied.
Theoretical Statistics is concerned with the
development, derivation and proof of statistical
theorems, formulae, rules and laws.
Applied Statistics involves the application of those
theorems, formulae, rules and laws to solve real-
world problems.
• This course will concentrate on Applied Statistics.10

10. Applied Statistics can be divided into two areas:
Descriptive Statistics consists of methods for
organizing, displaying and describing data by
using tables, graphs and summary measures.
Inferential Statistics consists of methods that
use sample results to help make decisions
or predictions about a population.
This course will cover aspects of both areas.
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11. Suppose we have information on the test results of students enrolled in a
statistics class
– Data set: the whole set of numbers that represent the scores of the
students
– Element: the name of each student
– Observation: score of each student
• A dataset is usually very large (for this course, 600-800 students!) and
therefore not very helpful in drawing conclusions or making decisions
• We therefore find ways to summarize the dataset into either tables,
diagrams, or numbers
• We will learn in this course how to construct tables, diagrams, graphs,
and how to calculate summary numerical measures such as averages,
variances and standard deviations.
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12. 13

13. What can you discern about these two data sets?
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14. Suppose you see a 6-foot lady walking down the street
• Your first thought? “she is tall for a lady”
• How did you come up with this? Do you have the height of every lady
on the planet?
• No! But based on your experience, of the women you have seen, this
particular one seems unusual. Why?
• This is an example of Inferential Statistics in daily life
• The required areas of knowledge of Inferential Statistics to be covered
in this course are as follows:
– Estimation;
– Tests of Hypotheses;
– Regression and Correlation Analysis.
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15. Population
– the collection of all elements of interest (all women)
Sample
– the selection of a few elements from this population is called a sample
(all women you have seen)
Inferential Statistics
– deals with making generalizations or inferences about populations
based on results obtained from samples (she is tall for a woman)
For example, the conclusions from the series of polls done in an
election year in Trinidad and Tobago
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16. Suppose that we wish to find answers to such questions as:
• Did the number of persons living below the poverty line decline over
the last decade?
• Are serious crimes more prevalent today than ten years ago?
These questions can only be answered by employing inferential
statistics, since in each case we need to go beyond the mere
description of the data in order to arrive at an inference.
• The corresponding questions for descriptive statistics would be:
– What was the number of persons living below the poverty line for
each year over the past decade?
– What was the level of serious crimes ten years ago and what is the
level today? 17

17. The ‘bridge’ between Descriptive Statistics and Inferential
Statistics is Probability Theory.
• Probability, which measures the likelihood that a certain
outcome occurs, is the basis of Inferential Statistics.
• The required areas of knowledge of Probability Theory to
be covered in this course are as follows:
– Axioms of Probability
– Laws of Probability
– Random Variables
– Discrete Probability Distributions
– Continuous Probability Distributions
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18. Population = all elements –individuals, items or
objects –whose characteristics are being
studied
Sample = a portion of the population selected
for study
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19. How do we collect information? Via a survey.
Census = a survey that includes every element of
the target population
Sample survey = a survey that collects
information from a portion of the population
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20. Specialized agencies exist in both the private and public sectors that
undertake the collection and dissemination of data. These include:
• Statistical Institute of Jamaica
• Central Statistical Office (Trinidad and Tobago)
• Central Banks (Trinidad and Tobago, Barbados, Jamaica, OECS etc)
• Planning Units/Ministries of Governments across the Caribbean
• Elections and Boundaries Commissions in each country of the
Caribbean
• CARICOM
• Association of Caribbean States (ACS)
• Organization of American States (OAS)
• CAREC
• PAHO/WHO
• UNESCO
• UNDP
• IADB
• World Bank. 21

21. Any statistical decision problem possesses five
components, namely:
• a clear specification of the question to be answered and
a clear definition of the data that is to be considered
• a decision on how to select a sample -the sampling
procedure and the design of the experiment
• the collection of data
• the establishment of a procedure for making inferences
(generalizations) about a population based on the
sample information
• a provision for measuring the goodness or reliability of
the inference. 22

22. Statistical Investigation
Conceptually, the activities involved in executing a statistical investigation can be
organized into four stages namely:
Experiment/Survey Design
• defining the population
• selecting the sampling method
• deciding on the sample size
• defining the data to be collected from the sample
• deciding on the form of collection
• designing an instrument for the collection of data.
Information Quantification
• data collection
• audit of data in the field
• coding of data
• audit of the coded data
• data entry to create the dataset
• validation of the dataset
• summary of data into tables and charts
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23. Statistical Investigation (cont’d)
Making the Inference
• select the appropriate method for making the
generalization
• computing the summary measures from the dataset
• making the generalization (inference) based on the
results of the sample survey
Reliability Attestation
• testing the inference to quantify the likelihood of error.
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24. Next Steps
• Each Lecture Outline will be posted onto the website on the
weekend, after the weekly lectures are complete.
• These are Lecture Outlines only, which means you have to use
these broad topics, read the relevant chapter in the Mann and do a
complete review.
• The Mann chapters all contain some excellent review questions that
you should attempt.
• The tutorial sheets will ask some questions on material that was not
explicitly covered in the lecture but is within the relevant Chapter of
the Mann.
• Read your textbook!
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