## Statistics For Economists (Paper 4) M.A. Part-I

The main objective of this course is to acquaint students with the basic techniques of statistical methods with strong emphasis on its application to economic theories and principles. The material covered in this course would enable students in not only testing the predictions of economic theories at an elementary level, but it would also help develop the basic skills necessary to take advanced courses like econometrics and growth models. Major topics covered in this course are measures of central tendency, probability, sampling design, estimation techniques, analysis of variance, non-parametric statistics, and Bayesian analysis. It is expected that after the completion of this course, students would be comfortable in handling and analyzing data and use of estimation techniques.

*No prerequisite for this course is required*. *However, basic knowledge of statistics will be an added advantage.*

**Topic 1: Introduction**

- Descriptive and inferential statistics;
- Variable and constant, population and sample, parameter and statistic;
- The four basic activities in statistics: Designing a plan for data collection, Exploring the data, Estimating an unknown quantity, Hypothesis testing;
- Type of measurement scales: Nominal, Ordinal, Interval and Ratio;
- Types of data: Univariate, Bivariate and Multivariate data, Primary and secondary data, Quantitative data and qualitative data, Time series, Cross- sectional and pooled data;
- Significant digits and rounding off numbers;
- Errors: Biased and unbiased.

**Topic 2: Presentation of Data and Measure of Central Tendency**

- Introduction; Classification; Tabulating numerical data:
- The frequency distribution, The cumulative frequency distribution, The relative frequency distribution, The percentage frequency distribution;
- Graphic and diagrammatic representation: Bar chart, Pie chart, Histograms, Frequency curves and Histo- grams; Histograms by Hand: Stem-and-leaf.
- Measure of central tendency; Introduction;
- Types of Averages: Mean: Arithmetic mean, Geometric mean, Harmonic mean, Trimmed mean and Winsorized mean; Quintiles: Median, Quartiles, Deciles, Percentiles;
- The mode;
- Box plot and detailed box plot;
- Empirical relation between Mean, Median and Mode;
- The cumulative distribution function: Finding the percentile ranking for a given number, Finding the percentile for a given percentage;
- Summary measures and type of data.

**Topic 3: Measures of Dispersion, Skewness and Kurtosis**

- Absolute and relative measure of dispersion;
- Different measures of dispersion: The Range, Quartile deviation, Mean deviation, Variance and standard deviation:
- Definition and interpretation of variance and standard deviation,
- Computation of variance and standard deviation, Step deviation method or coding method,
- Coefficient of variation,
- Standardized variable,
- Properties of standard deviation and variance;
- Skewness: Karl Pearson’s coefficient of skewness, Bowley’s coefficient of skewness;
- Kurtosis.

**Topic 4: Probability and Probability Distribution**

- A survey of probability concepts: Classical probability, Empirical concept, Subjective probability;
- Some rules of probability: Rules of addition, Rules of multiplication;
- Tree diagrams;
- Conditional Probability,
- Bayes Theorem;
- Counting rules: The multiplication formula, The permutation formula, The combination formula.
- Discrete probability distribution,
- Random variables,
- Discrete random variable,
- Continuous random variable;
- The mean, variance and standard deviation of a probability distribution;
- Binomial probability distribution, and its computation.
- Cumulative probability distributions,
- Properties of Binomial probability distribution.
- The normal probability distributions:
- Properties of normal distribution,
- Applications of the standard normal distribution,
- Areas under the normal curve,
- Finding areas under the normal curve;
- The normal approximation to the binomial;
- Continuity correction factor.

**Topic 5: Survey Sampling and Sampling Distributions**

- Sampling the population,
- Advantages of sampling,
- Representative samples,
- Sample design and sample survey,
- Sampling frame,
- Probability and non- probability sampling,
- Sampling with and without replacement,
- Sampling and non-sampling error,
- sampling bias;
- Probability sampling and non-probability sampling methods;
- Sampling distribution of the mean;
- The central limit theorem;
- Sampling distribution of differences between means;
- Sampling distribution of sample proportion;
- Sampling distribution of differences between proportions.

**Topic 6: Estimation and Confidence Intervals**

- Point estimates and confidence intervals;
- Estimation by confidence interval:
- Confidence interval estimate of a population mean (Known Variance),
- Confidence interval estimate of a population mean (Unknown Variance)
- Confidence interval for differences of means,
- Confidence interval for differences of means;
- Confidence interval for population proportion,
- Confidence interval for differences between proportions;
- One sided confidence interval;
- Sample size for estimating population mean.

**Topic 7: Hypothesis Testing**

- One sample test of hypothesis;
- One Sample; One tail and two tails tests of significance;
- Testing for a population mean with a known population standard deviation:
- Two-tailed test, one-tailed test;
- P-Value in hypothesis testing;
- Testing for a population mean: Large sample, Population standard deviation unknown;
- Testing hypotheses about population proportion when sample size is large;
- Type II error.
- Testing of two Sample Hypothesis: Population means, Population proportions; comparing populations with small samples.

**Topic 8: Chi Square Applications**

- Introduction;
- Goodness-of-fit test:
- Equal expected frequencies;
- Goodness-of-fit test:
- Unequal expected frequencies;
- Limitations of Chi square;
- Using the goodness-of-fit test to test for normality;
- Contingency Table Analysis.

**Topic 9: Analysis of Variance**

- Introduction,
- The F distribution;
- Comparing two population variances;
- ANOVA assumptions; ANOVA test;
- Inferences about pairs of treatment means;
- Two-way analysis of variance.

**Topic 10: Simple Linear Regression and Correlation Analysis**

- Scatter diagram;
- Standard methods for obtaining regression line: (
*i*) Inspection, - (
*ii*) Semi average, (*iii*) Least squares principle; - Assumptions underlying linear regression;
- Measures of variation: Standard error of the estimate,
- Coefficient of determination;
- Prediction in Regression Analysis;
- Interpolation verses extrapolation;
- Correlation analysis; Scatter diagram;
- The coefficient of correlation:
- Properties/characteristic of coefficient of correlation,
- Correlation and causation;
- The relationship among the correlation coefficient, the coefficient of determination and the standard error of estimate;
- Inference about the slope and correlation coefficient;
- t-test for the slope,
- F- test for the slope,
- t-test for correlation coefficient;
- Estimation of the mean values and predication of individual values;
- Confidence interval and predication interval estimate;
- Rank correlation.

**Topic 11: Multiple Linear Regression and Correlation Analysis**

- Multiple linear regression model,
- Interpretation of partial regression coefficients;
- Estimation of multiple linear regression model with two explanatory variables by using Least squares principle,
- Matrix approach, Deviation form;
- Pitfalls and problems in multiple regression:
- Multicollinearity,
- Variable selection,
- Model misspecification;
- Multiple standard error of estimate;
- Coefficient of multiple determination (adjusted and unadjusted);
- Evaluating the regression equation:
- Using a scatter diagram,
- Correlation matrix,
- Global test,
- Individual variable significance test,
- Qualitative independent variables;
- Multiple regressions in terms of linear correlation coefficients;
- Multiple correlation and partial correlation;
- Nonlinear regression models;
- Dealing with nonlinear relationship and unequal variability.

**Topic 12: Applied Statistics**

- Index Numbers, Un-weighted index numbers; Simple aggregative index; Weighted indexes;
- Laspeyre’s price index,
- Paaseche’s price index,
- Marshal- Edgeworth price index;
- Fisher’s ideal index;
- Consumer Price Index (CPI),
- Producer Price Index (PPI),
- CPI versus GDP Deflator;
- Issues in constructing and using index numbers;
- Application of index numbers to business and economics.
- An overview of time series analysis;
- Component Factors of the classical multiplication time series model and their estimation:
- Secular trend;
- Cyclical variation,
- Seasonal variation,
- Irregular variation;
- Smoothing the annual time series and using it in forecasting:
- Moving averages,
- Weighted moving averages,
- Exponential smoothing;
- Using trend and seasonal component in forecasting;
- Time series and forecasting;
- The multiplicative model,
- Calculating the seasonal indexes,
- De-seasonalization the time series,
- Using deseasonalized time series to identify trend,
- Seasonal adjustments,
- Model based on monthly data,
- Cyclical component; Modeling cyclic behavior using box-Jenkins
- ARIMA processes; Using regression analysis in forecasting;
- Qualitative approach to forecasting: Delphi method, Expert judgment, Scenario writing, Intuitive approaches;
- Choosing an appropriate forecasting model; Some observations on time series analysis.

### Recommended Text books:* *

- Lind, Douglas A., Marshal, William G. and Mason, Robert D.,
*Statistical Techniques in Business and Economics*(11th edition). Boston: McGraw Hill, - Chaudhry, Sher Mohammad and Kamal, Shahid,
*Introduction to Statistical Theory*(7th edition). Lahore: Ilmi Kitab Khana, - Siegel, Andrew F.,
*Practical Business Statistics*(5th edition). Boston: McGraw Hill, 2003. - Newbold, Paul, Carlson, William L. and Thorne, Betty M,
*Statistics for Business and Economics*(5th edition). New Jersey: Prentice Hall, - Keller, Gerald and Warrack, Brian,
*Statistics for Management and Economics*(5th edition). Boston: Duxbury Thomson Learning,

### Additional Readings:

- Berenson, Mark L., Levine, David M. and Krehbiel, Timothy C.,
*Basic Business Statistics*:*Concepts and Applications*(9th edition). New Jersay: Prentice Hall, - Barron, Michael M., Statistics for Economics Accounting and Business Studies (Latest Edition), New York, Prentice
- Carlson, William L. and Thorne, Betty,
*Applied Statistical Methods for Business Economics and Social Sciences*(Latest edition). New Jersey: Prentice - Moore, David S.,
*The Basic Practice of Statistics*(2nd edition). New York: Freeman,2000.

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