**Paper 4. STATISTICS FOR ECONOMISTS**

**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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