Intro to Statistics-Lecture One Flashcards
we got this
Statistics
–Numerical facts
–The field or discipline of study
Statistics as a field of study
is a group of methods used to collect, analyse, present and interpret data and to make decisions.
How can statistics help us?
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”
Why study Statistics?
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.
Branches or Aspects of Statistics
Theoretical and Applied
Theoretical Statistics
is concerned with the development, derivation and proof of statistical theorems, formulae, rules and laws
Applied Statistics
involved the application of those theorems, formulae, rules and laws to solve real-world problems.
Types of Applied Statistics
Descriptive and Inferential Statistics
Descriptive Statistics
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
Inferential Statistics
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
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.
Population and Sample in Inferential Statistics
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
When would we use inferential or descriptive statistics?
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?
What is the bridge between Descriptive and Inferential Statistics?
Probability Theory
Probability
which measures the likelihood that a certain outcome occurs, is the basis of Inferential Statistics.
Areas of Probability Theory
Axioms of Probability
–Laws of Probability
–Random Variables
–Discrete Probability Distributions
–Continuous Probability Distributions
Population vs Sample
Population = all elements –individuals, items or objects –whose characteristics are being studied
*Sample = a portion of the population selected for study
Census vs Sample 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
Representative Sample
a sample that represents the characteristics of the population as closely as possible.
User and Suppliers of Statistics
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.
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
Profit & Loss Statements,
*Balance Sheets,
*Budgets, and
*Project Reports.
The statistics generated by the specialized agencies are used by various
professionals in the pursuit of their disciplines/areas of specialty. These
include:
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;
Statistical Investigations and Decision Problems
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.
Statistical Investigation
- 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
27 - 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.
Variable
a characteristic under study that assumes different values for different elements. In contrast, the value of a constant is fixed
Observation or measurement
the value of a variable for an element
A data set
is a collection of observations on one or more variables
Types of variables
Quantitative, Qualitative, Discrete and Continuous
Quantitative and Qualitative Variables
Variable can be measured numerically whereas others cannot
Quantitative data
the data collected on a quantitative variable
Discrete variables
a variable that assumes countable values or only certain values with no intermediate values
Continuous variables
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
qualitative or categorical variable
values that cannot be measured numerically but can be divided into different categories
Name two organizations in the Caribbean that collect, summarize and publish Demographic data
Caribbean Development Bank, National Statistical Institute of Trinidad and Tobago
Two organizations in the Caribbean that collect, summarize and publish socioeconomic data
World bank world development indicators
