Statistical Methods for Economics

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.