Intro to Statistics-Lecture One

Question 1

Statistics

Answer 1

–Numerical facts
–The field or discipline of study

Question 2

Statistics as a field of study

Answer 2

is a group of methods used to collect, analyse, present and interpret data and to make decisions.

Question 3

How can statistics help us?

Answer 3

Every day we are confronted by the need to make decisions.
*These decisions are made under conditions of uncertainty, with no precise or definite solution (shall I take a 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”

Question 4

Why study Statistics?

Answer 4

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) has led to an unprecedented ‘data explosion’in which we are subjected to a barrage of economic figures and claims about product superiority.
*Statistical analyses now influence the availability of a wide range of goods and services.

Question 5

Branches or Aspects of Statistics

Answer 5

Theoretical and Applied

Question 6

Theoretical Statistics

Answer 6

is concerned with the development, derivation and proof of statistical theorems, formulae, rules and laws

Question 7

Applied Statistics

Answer 7

involved the application of those theorems, formulae, rules and laws to solve real-world problems.

Question 8

Types of Applied Statistics

Answer 8

Descriptive and Inferential Statistics

Question 9

Descriptive Statistics

Answer 9

Descriptive Statistics consists of methods for organising, displaying and describing data by using tables, graphs and summary measures.
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

Question 10

Inferential Statistics

Answer 10

consists of methods that use sample results to help make decisions or predictions about a population. Suppose you see a 6-foot woman walking down the street
*Your first thought? “she is tall for a woman”
*How do you come up with this? Do you have the height of every woman 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

Question 11

The required areas of knowledge of Inferential Statistics to be covered in this course are as follows:

Answer 11

Estimation;
–Tests of Hypotheses;
–Regression and Correlation Analysis.

Question 12

Population and Sample in Inferential Statistics

Answer 12

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 generalisationsor 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

Question 13

When would we use inferential or descriptive statistics?

Answer 13

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?

Question 14

What is the bridge between Descriptive and Inferential Statistics?

Answer 14

Probability Theory

Question 15

Probability

Answer 15

which measures the likelihood that a certain outcome occurs, is the basis of Inferential Statistics.

Question 16

Areas of Probability Theory

Answer 16

Axioms of Probability
–Laws of Probability
–Random Variables
–Discrete Probability Distributions
–Continuous Probability Distributions

Question 17

Population vs Sample

Answer 17

Population = all elements –individuals, items or objects –whose characteristics are being studied
*Sample = a portion of the population selected for study

Question 18

Census vs Sample Survey

Answer 18

Census = a survey that includes every element of the target population
*Sample survey = a survey that collects information from a portion of the population

Question 19

Representative Sample

Answer 19

a sample that represents the characteristics of the population as closely as possible.

Question 20

User and Suppliers of Statistics

Answer 20

Statistical Institute of Jamaica
*Central Statistical Office (Trinidad and Tobago)
*Central Bank of Trinidad and Tobago
*Central Bank of Barbados
*Central Bank of Jamaica
*Central Bank of the OECS
*Planning Units/Ministries of Governments across the Caribbean
*Elections and Boundaries Commissions in each country of the Caribbean
*CARICOM
*Association of Caribbean States (ACS)
*Organisationof American States (OAS)
*CAREC
*PAHO/WHO
*UNESCO
*UNDP
*IADB
*World Bank.

Question 21

Units like the Management Accounting Unit of some firms and Project Management Units of private sector and public sector organisations also undertake data collection and descriptive statistical work on a monthly, quarterly and annual basis. The output of these units takes the form of

Answer 21

Profit & Loss Statements,
*Balance Sheets,
*Budgets, and
*Project Reports.

Question 22

The statistics generated by the specialized agencies are used by various
professionals in the pursuit of their disciplines/areas of specialty. These
include:

Answer 22

Pollsters who may interview a predetermined number of persons in a country, record and count their preferences for a particular political candidate or party, and make a prediction about the outcome of an election based on the count;
*Market Researchers who may undertake a survey to determine what proportion of households prefer a brand of baking flour;
*Sociologists who may be interested in finding out what proportion of rural families include a graduate of tertiary education;
*Psychologists who may be interested in finding out whether deviant behaviourin the school system is linked to the occupational status of the head of household;
*Product Development Specialists who may be interested what proportion of commercial firms would be interested in purchasing a new product being developed by a local manufacturer, and if so, at what price;

Question 23

Statistical Investigations and Decision Problems

Answer 23

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 (generalisations) about a population based on the sample information
*a provision for measuring the goodness or reliability of the inference.

Question 24

Statistical Investigation

Answer 24

1. 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.
2. 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
   27
3. 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
4. Reliability Attestation
   *testing the inference to quantify the likelihood of error.

Question 25

Variable

Answer 25

a characteristic under study that assumes different values for different elements. In contrast, the value of a constant is fixed

Question 26

Observation or measurement

Answer 26

the value of a variable for an element

Question 27

A data set

Answer 27

is a collection of observations on one or more variables

Question 28

Types of variables

Answer 28

Quantitative, Qualitative, Discrete and Continuous

Question 29

Quantitative and Qualitative Variables

Answer 29

Variable can be measured numerically whereas others cannot

Question 30

Quantitative data

Answer 30

the data collected on a quantitative variable

Question 31

Discrete variables

Answer 31

a variable that assumes countable values or only certain values with no intermediate values

Question 32

Continuous variables

Answer 32

a variable that can assume any numerical value over a certain interval or intervals, keep going forever, not a precise value
E.g time, speed, weight, height

Question 33

qualitative or categorical variable

Answer 33

values that cannot be measured numerically but can be divided into different categories

Question 34

Name two organizations in the Caribbean that collect, summarize and publish Demographic data

Answer 34

Caribbean Development Bank, National Statistical Institute of Trinidad and Tobago

Question 35

Two organizations in the Caribbean that collect, summarize and publish socioeconomic data

Answer 35

World bank world development indicators