This is a course on Statistical methods for economics. This course aims to train the students to use the techniques of statistical analysis, which are commonly applied to understand and analyse economic problems. It begins with some basic concepts and terminology that are fundamental to study and understand statistical analysis and inference. It explains summarizing the measures such as measures of central tendency, dispersion, population moments and explains need and their properties and applications in the area of economic theory. It then develops the notion of probability, followed by random variables and their distributions in discrete and continuous cases, joint distributions, their properties, some commonly used distributions such as uniform, Binomial, Normal, Poisson and exponential distributions, their properties and applications. The course introduces sampling techniques, their need and different methods of drawing sampling. . At the end some topics are covered on statistical inference that include concepts of point and interval estimation their applications and uses.
Overview
Syllabus
Course Title: Statistical Methods for Economics for UG Economics subject
(Level & Subject) Syllabus (Based on Choice Based Credit System)
Unit
Week
Video
Title of Video and Reading text/Lecture/ppt
INTRODUCTION TO STATISTICS, FREQUENCY DISTRIBUTION, GRAPHICAL PRESENTATION, MEASURES OF CENTRAL TENDENCY
WEEK-1
Day 1
Introduction to Statistics and Economics.
Ø Introduction – Definition, Characteristics and limitations
Ø Scope of Statistics in Economics – Situations or examples
Ø Terminologies of Statistics with examples
Ø Scales of measurement – properties and classification
Ø Data collection methods
Day 2
Organization of the data.
Ø Classification of the data
Ø Tabulation of the data
Ø Frequency distribution – Terminologies
Ø Frequency distribution – univariate
Ø Frequency distribution – Bi-variate
Day 3
Graphical presentation of the data.
Ø Histogram – equal and unequal width
Ø Frequency curve – with and without histogram
Ø Frequency polygon – with and without histogram
Ø Ogive – less than and more than ogive
Ø Scatter plot
Day 4
Measures of Central Tendency – Part-I.
Ø Introduction – meaning, characteristics, limitations, various measures of central tendency
Ø Applications of central tendency in field of economics-with examples
Ø Computation of arithmetic mean-raw data
Ø Computation of arithmetic mean-discrete data
Ø Computation of arithmetic mean-continuous data
MEASURES OF CENTRAL TENDENCY AND MEASURES OF DISPERSION
WEEK-2
Day 1
Measures of Central Tendency – Part-II.
Ø Partition values – Meaning, properties, various partition values
Ø Median – Raw data (odd and even number of observations), discrete and continuous frequency distribution. Graphical location.
Ø Quartiles – Raw data, discrete and continuous frequency distribution
Ø Deciles - Raw data, discrete and continuous frequency distribution
Ø Percentiles - Raw data, discrete and continuous frequency distribution
Day 2
Measures of Central Tendency – Part-III.
Ø Mode – Meaning, properties.
Ø Computation of mode – raw data, discrete frequency distribution.
Ø Computation of mode-continuous frequency distribution.
Ø Empirical relationship of mode.
Ø Graphical location of mode.
Day 3
Measures of Dispersion – Part-I.
Ø Introduction – meaning, characteristics, limitations, absolute and relative measures, various measures of dispersion, importance of dispersion in the field of economics.
Ø Range – meaning, properties, application, computation for raw data (absolute and relative measure)
Ø Computation of range for discrete and continuous frequency distribution.
Ø Lorenz Curve and its interpretation
Ø Gini’s co-efficient and its interpretation
Day 4
Measures of Dispersion – Part – II.
Ø Quartile deviation - meaning, properties, computation in case of raw data, discrete and continuous frequency distribution
Ø Average deviation (mean) – meaning, properties, computation in case of raw data.
Ø Average deviation (mean) – computation for discrete and continuous frequency distribution.
Ø Average deviation (median) – computation in case of raw data.
Ø Average deviation (median) – computation for discrete and continuous frequency distribution.
MEASURES OF DISPERSION AND CONCEPT OF PROBABILITY
WEEK-3
Day 1
Measures of Dispersion – Part – III.
Ø Standard deviation – meaning, properties, computation in case of raw data.
Ø Standard deviation – computation for discrete frequency distribution
Ø Standard deviation – computation for continuous frequency distribution
Ø Variance and co-co-efficient of variation
Ø Application of standard deviation in economics
Day 2
Skewness, Kurtosis and Moments.
Ø Concept of moments, moments about mean, arbitrary point, origin,
Ø Skewness – Concept, types, methods of skewness.
Ø Computation of skewness-Karl Pearson’s and Bowley’s method.
Ø Kurtosis – concept, type.
Ø Skewness and Kurtosis based on moments
Day 3
Concept of Probability.
Ø Introduction to concept of probability
Ø Terminologies and notations associated with probability.
Ø Construction of sample space and events
Ø Classical probability – concept + Activity
Ø Empirical probability
Day 4
Probability Axioms – I.
Ø Addition theorem of probability of dependent events
Ø Addition theorem of probability of independent events
Ø Addition theorem of probability of mutually exclusive events
Ø Concept of conditional probability
Ø Activity – 1
PROBABILITY THEORY, RANDOM VARAIBLE AND MATHEMATICAL EXPECTATION
WEEK-4
Day 1
Probability Axioms – II.
Ø Multiplication theorem of probability of dependent events
Ø Multiplication theorem of probability of independent events
Ø Important results on probability of events (Conditional events)
Ø Activity – 1
Ø Activity - 2
Day 2
Inverse Probability (Baye’s Theorem).
Ø Rule of Inverse probability
Ø Activity - 1
Ø Tree-Diagram method of solution
Ø Activity-2
Ø Activity-3
Day 3
Random Variable and Probability Distribution.
Ø Concept of a random variable and random experiment.
Ø Probability distribution of a discrete random variable.
Ø Probability distribution of a continuous random variable.
Ø Activity -1 (discrete random variable).
Ø Activity-2 (continuous random variable).
Day 4
Mathematical Expectation of a random variable.
Ø Definition of mathematical expectation.
Ø Theorems / Properties of mathematical expectation.
Ø Mathematical expectation of a discrete and continuous random variable.
Ø Mathematical expectation of a function of the random variable.
Ø Activity-1.
DISCRETE THEORETICAL DISTRIBUTIONS
WEEK-5
Day 1
Introduction to theoretical distributions.
Ø Introduction to theoretical distributions.
Ø Concept of discrete theoretical distributions.
Ø Concept of continuous theoretical distributions.
Ø Importance of theoretical distributions in economics.
Ø Activity - 1
Day 2
Discrete Uniform distribution.
Ø Concept and definition of discrete uniform distribution.
Ø Properties / features of discrete uniform distribution.
Ø Computation of discrete uniform probabilities-1 (using density function)
Ø Computation of discrete uniform probabilities -2 (using distribution function)
Ø Application of discrete uniform distribution in economics.
Day 3
Binomial Distribution.
Ø Concept and definition of binomial distribution.
Ø Properties / features of binomial distribution.
Ø Computation of binomial probabilities (using density and distribution function),
Ø Fitting of a binomial distribution.
Ø Application of binomial distribution in economics.
Day 4
Poisson Distribution.
Ø Concept and definition of Poisson distribution.
Ø Properties / features of Poisson distribution.
Ø Computation of Poisson probabilities (using density and distribution function).
Ø Fitting of Poisson distribution.
Ø Application of Poisson distribution in Economics.
CONTINUOUS THEORETICAL DISTRIBUTION
WEEK-6
Day 1
Continuous Uniform Distribution.
Ø Concept and definition of continuous uniform distribution.
Ø Properties / features of continuous uniform distribution.
Ø Computation of continuous uniform probabilities-1 (using density function)
Ø Computation of continuous uniform probabilities -2 (using distribution function)
Ø Application of continuous uniform distribution in economics.
Day 2
Exponential Distribution.
Ø Concept and definition of exponential distribution.
Ø Properties / features of exponential distribution.
Ø Computation of exponential probabilities-1 (using density function).
Ø Computation of exponential probabilities-2 (using distribution function).
Ø Application of exponential distribution in economics.
Day 3
Normal Distribution-1.
Ø Concept and definition of normal distribution.
Ø Properties / features of normal distribution.
Ø Reading of normal table.
Ø Application of normal distribution in economics.
Day 4
Normal Distribution-II.
Ø Computation of normal probabilities-1 (using density function)
Ø Computation of normal probabilities-2 (using distribution function)
Ø Fitting of normal distribution
Ø Generating random samples from normal distribution
BIVARIATE RANDOM VARIABLE AND ITS MATHEMATICAL EXPECTATION
WEEK-7
Day 1
Bi-variate random variable.-Discrete
Ø Concept of a discrete bi-variate random variable.
Ø Bi-variate density functions of a discrete random variable.
Ø Bi-variate distribution function of a discrete random variable
Ø Problems on bi-variate discrete random variable
Ø Uses of bi-variate discrete random variable in economics
Day 2
Bi-variate random variable.-Continuous
Ø Concept of a continuous bi-variate random variable.
Ø Bi-variate density functions of a continuous random variable.
Ø Bi-variate distribution functions of a continuous random variable.
Ø Problems on bi-variate continuous random variable.
Ø Uses of bi-variate continuous random variable in economics.
Day 3
Marginal and Conditional distribution.
Ø Marginal distribution - discrete random variable
Ø Marginal distribution – continuous random variable
Ø Conditional distribution- discrete random variable
Ø Conditional distribution-continuous random variable
Ø Properties of marginal and conditional distributions
Day 4
Mathematical Expectation of a Bi-variate random variable
Ø Concept of mathematical expectation of a bi-variate random variable.
Ø Addition theorem on mathematical expectation. (Discrete and Continuous)
Ø Multiplication theorem on mathematical expectation. (Discrete and Continuous)
Ø Properties of mathematical expectation of a bi-variate random variable.
Ø Application of mathematical expectation in economics.
MARGINAL AND CONDITIONAL EXPECTATION AND SAMPLING
WEEK-8
Day 1
Marginal and Conditional Expectation.
Ø Marginal expectation - discrete random variable
Ø Marginal expectation – continuous random variable
Ø Conditional expectation- discrete random variable
Ø Conditional expectation-continuous random variable
Ø Properties of marginal and conditional expectations
Day 2
Mathematical Expectation – Covariance and correlation
Ø Covariance using mathematical expectation.
Ø Correlation using mathematical expectation.
Ø Interpretation of the correlation value.
Ø Activity on correlation analysis.
Ø Application of correlation analysis in economics.
Day 3
Sampling
Ø Concept and definition of sampling.
Ø Terminologies in sampling.
Ø Principle steps in sample survey.
Ø Methods of sampling – advantages and disadvantages.
Ø Sampling Errors.
Day 4
Non Probability Sampling Techniques
Ø Introduction to non-probability sampling techniques, merits and demerits.
Ø Convenience sampling - introduction, merits and demerits.
Ø Judgement sampling – introduction, merits and demerits.
Ø Quota sampling – introduction, merits and demerits.
Ø Snowball or network sampling – introduction, merits and demerits.
SAMPLING TECHNIQUES AND THEORY OF ESTIMATION
WEEK-9
Day 1
Simple Random Sampling
Ø Introduction to simple random sampling
Ø Methods of simple random sampling
Ø Results / characteristics of simple random sampling
Ø Advantages and disadvantages of simple random sampling
Ø Situations where simple random sampling is applicable
Day 2
Stratified Random Sampling
Ø Introduction to stratified random sampling
Ø Types of stratified random sampling
Ø Results / characteristics of stratified random sampling
Ø Advantages and disadvantages of simple random sampling
Ø Situations where stratified random sampling is applicable
Day 3
Other random sampling techniques.
Ø Systematic random sampling
Ø Cluster random sampling
Ø Multistage sampling
Ø Multiphase sampling
Ø Situation where systematic, cluster, multistage, multiphase sampling techniques are applicable.
Day 4
Theory of Estimation
Ø Introduction of theory of estimation
Ø Terminologies used in estimation
Ø Unbiasedness +Activity
Ø Consistency + Activity
Ø Efficiency + Activity
POINT ESTIMATION
WEEK-10
Day 1
Point estimation – methods of moments (Discrete)
Ø Introduction – Steps involved in estimation for discrete random variable
Ø Binomial distribution-1
Ø Binomial distribution-2
Ø Poisson distribution-1
Ø Poisson distribution-2
Day 2
Point estimation – methods of moments (Continuous)
Ø Introduction – Steps involved in estimation for continuous random variable.
Ø Continuous Uniform distribution
Ø Exponential distribution
Ø Normal distribution-1
Ø Normal distribution-2
Day 3
Point estimation – maximum likelihood procedure (Discrete)
Ø Introduction – Steps involved in estimation for discrete random variable
Ø Binomial distribution-1
Ø Binomial distribution-2
Ø Poisson distribution-1
Ø Poisson distribution-2
Day 4
Point estimation – maximum likelihood procedure (Continuous)
Ø Introduction – Steps involved in estimation for continuous random variable.
Ø Continuous Uniform distribution
Ø Exponential distribution
Ø Normal distribution-1
Ø Normal distribution-2
INTERVAL ESTIMATION
WEEK-11
Day 1
Interval estimation – I
Ø Concept and terminologies associated with interval estimation
Ø Construction of confidence interval for mean – variance known
Ø Activity on construction of confidence interval for mean – variance known
Ø Construction of confidence interval for mean – variance unknown
Ø Activity on construction of confidence interval for mean – variance unknown
Day 2
Interval estimation – II
Ø Construction of confidence interval for difference of mean – variance known
Ø Activity on construction of confidence interval for difference of mean – variance known
Ø Construction of confidence interval for difference of mean – variance unknown
Ø Activity on construction of confidence interval for difference of – variance unknown
Day 3
Interval estimation - III
Ø Construction of confidence interval for variance – mean known
Ø Construction of confidence interval for variance – mean unknown
Ø Construction of confidence interval for ratio of variance – mean known
Ø Construction of confidence interval for ratio of variance – mean unknown
Ø Activity on confidence interval for variance and ratio of variance.
Day 4
Interval estimation - IV
Ø Construction of confidence interval for single proportion.
Ø Construction of confidence interval for difference of proportion.
Ø Activity on confidence interval for proportion.
Ø Construction of confidence interval for correlation coefficient.
Ø Activity on confidence interval for correlation coefficient.
APPLICATION TOOLS OF STATISTICS
WEEK-12
Day 1
Sample size determination
Ø Sample size using mean and standard deviation from pilot study
Ø Sample size using prevalence from pilot study.
Ø Sample size for finite and infinite population
Ø Case studies
Day 2
Questionnaire Preparation.
Ø Case study: Data on reality shows
Ø Construction of Questionnaire
Ø Excel entries with coding for the data
Day 3
Validity and Reliability
Ø Validity – Definition, purpose
Ø Different types of validity
Ø Reliability-Definition, purpose
Ø Different types of reliability
Ø Comparison between validity and reliability
DESCRIPTIVE STATISTICS AND PROBABILITY COMPUTATION FROM STANDARD DISTRIUTIONS USING MS EXCEL AND CONCLUSION.
Day 1
Descriptive Analysis – Using MS Excel
Ø Frequency tables for raw data
Ø .Graphs
Ø Measures of central tendency
Ø Measures of dispersion
Ø Correlation Analysis
WEEK-13
Day 2
Probability Distributions –Using MS Excel
Ø Binomial distribution
Ø Poisson distribution
Ø Continuous uniform
Ø Exponential
Ø Normal
Day 3
Summarization of the whole concept with an example.
Taught by
Prof. Vidya R
