Module Code and Title:       QME102         Statistical Methods in Economics

Programme:                          BA in Development Economics

Credit Value:                         12

Module Tutor:                       Sonal Mehta

General objective: The module introduces some basic concepts and terminology that are fundamental to statistical analysis and inference relevant to the study of economics. It develops the notion of probability, and probability distributions of discrete and continuous random variables. This module will help students to summarize data, analyse empirical relationships, test theories, and make predictions. The module introduces students to statistical tools, e.g., hypothesis testing and parameter estimation. The main intent is to enable students to understand how statistical procedures are used to summarize information.

Learning outcomes – On completion of this module, learners should be able to:

1. Identify different levels of data.
2. Set up sample data for a simple statistical analysis.
3. Use spreadsheets for data mining.
4. Present data and interpret results.
5. Explain probability theory.
6. Discuss the significance of common statistical measures, e.g., mean, skewness and range.
7. Interpret the output of simple linear regression and correlation analyses.
8. Distinguish between normal, Poisson and binomial distributions.
9. Explain confidence intervals and p values.
10. Formulate null and alternative hypotheses.
11. Construct graphical displays using spreadsheets.

Learning and Teaching Approach: Lecture, tutorials, laboratory work and group work will be used as primary activities for teaching and learning. The module tutor shall use direct instruction for explaining the rules and procedures for solving problems in the class lectures, and use a conceptual approach to convey why particular formulae and processes of solutions work. Focus should be on the interpretation of output derived using statistical software, e.g. from spreadsheets. The lectures will be complemented with tutorials. Students will use a computer laboratory to learn the use of spreadsheets for data analysis. Group work will focus on collective learning and problem solving.

Assessment Approach:

A. Individual Assignment: Portion of Final Marks: 10%

The assignment will assess the ability of students to discuss the significance of statistical measures, identify when they are applied, and point out their shortcomings. The assignment should have a maximum limit of 250 words.

• 4%       Clearly outline the significance of each measure
• 3%       Explain when each measure is used
• 2%       Identify any shortcomings
• 1%       Provide relevant examples to support arguments

B. Class Tests: Portion of Final Marks: 20%

Four written tests will be conducted (worth 5%, two prior to and two after the mid-semester), that will comprise 45 min duration and cover 2-3 weeks of material. The tests will contain 5 questions (3 on the conceptual understanding and 2 on problem solving).

D. Practical Exercise: Portion of Final Mark: 15%

The task is for each student to clean and arrange the given raw data and provide a descriptive and graphical analysis, as a form of “data mining”. The tutor will provide raw data for the work. Students should use spreadsheets for this work.

• 2%       Data cleaning
• 3%       Arrangement of raw data for analysis
• 6%       Clearly communicate the analysis of results- descriptive and inferential statistics
• 4%       Construction of appropriate graphs to represent the analysis

E. Midterm Examination: Portion of Final Mark: 15%

Students will take a written exam of 1.5 hr duration covering topics up to the mid-point of the semester.

Pre-requisites:

Subject matter:

1. Introduction
   • Nature and use of statistics
   • Statistical challenges and pitfalls
2. Data Collection:
   • Level of measurement: nominal, ordinal, interval and ratio
   • Time series date, cross sectional data and panel data
   • Sampling concept: population, sample, sample frame, required sample size, basic methods for selecting samples, sampling and non-sampling error, non-response
3. Visual Description of Data
   • Dot plots, frequency distribution and histograms and frequency polygons, ogives
   • Line charts, bar charts, scatter plot and pie charts
4. Descriptive Statistics
   • Central tendency: Mean- Simple, weighted, harmonic and geometric, median and mode, relation between AM, GM and HM, quartiles, deciles and percentiles
   • Dispersion: Range, inter quartile range, mean deviation, standard deviation, variance, Chebyshev theorem, coefficient of variation
   • Standardized data, percentiles and quintiles
   • Moments, skewness and kurtosis
5. Probability
   • Random experiments, counting rule and probability
   • Rules of probability
   • Independent events
   • Contingency tables and tree diagram
   • Conditional probability- independent events and multiplication law
   • Bayes theorem, tabular approach
   • Counting rule
6. Discrete Distribution
   • Random variables- discrete and continuous
   • Probability model
   • Discrete and uniform distribution
   • Expected value and variance
   • Binomial and Poisson distribution
7. Sampling
   • Random samples and random numbers
   • Sampling with and without replacement
   • Sampling distribution of means and proportions
   • Unbiased and efficient estimates, point and interval estimates, their reliability, confidence interval estimates of population parameters, probable error
8. Statistical Decision Theory (focus should be interpretation of the results, ie- MS Excel output of the tests and not the computation).
   • Statistical hypothesis
   • Decision rule- test of hypothesis, type I and type II errors, level of significance
   • Two tailed and one tailed tests, p-value for hypothesis test
   • Small sampling theory- students t test, chi-square test, confidence interval for σ, Degrees of freedom and F distribution
9. Association (focus should be interpretation of the results, ie- spreadsheet output of the tests and not the computation)
   • Bivariate correlation- types, correlation and causation, scatter plot diagram, Pearson coefficient of correlation, probable error, rank correlation, coefficient of determination
   • Bivariate regression – best fit line, regression of Y on X and regression of X on Y, making prediction, coefficient of regression, standard error of estimate
10. Index Number
    • Introduction- types, problems in construction, methods of construction- unweighted and weighted
    • Test of consistency: unit test, time reversal and factor reversal
    • Indices: chain indices, base shifting, splicing, cost of living index, deflation

Reading List:

1. Essential Reading
   • Doane, D. & Seward, L. (2010). Applied Statistics in Business and Economics. McGraw-Hills/Irwin.
   • Newbold, P., Carlson, W. & Thorne, B. (2012). Statistics for Business and Economics. Pearson Education.
2. Additional Reading
   • Devore, J.L. (2010). Probability and Statistics for Engineers. Cengage Learning.
   • Larsen, R.J. & Marx, M.L. (2011). An Introduction to Mathematical Statistics and its Applications. Prentice Hall.
   • Spiegel M.L. & Stephens, L. J. (2007). Statistics, Schaum Outline Series. McGraw Hills.

Date: January 15, 2016