Quantitative Methods
Aims
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Achieve an overall understanding of how and why statistics and mathematics are used in economic and business decisions.
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Demonstrate the ability to collect, present, analyse and interpret quantitative data using standard statistical techniques.
Programme Content and Learning Objectives:
After completing the programme the student should be able to:
1. Demonstrate an overall understanding of the data collection process.
This includes sources of data, sampling methods, problems associated with surveys, questionnaire design, measurement scales (nominal, ordinal, interval and ratio scales) and sampling error.
2. Use a range of descriptive statistics to present data effectively.
This includes the presentation of data in tables and charts, frequency and cumulative frequency distributions and their graphical representations, measures of location, dispersion and skewness, index numbers and their applications.
3. Understand the basic concepts of probability and probability distributions.
This includes the basic ‘rules’ of probability, expected values and the use of probability and decision trees, the binomial and Poisson distributions and their applications, and the characteristics and use of the normal distribution.
4. Apply the normal distribution and the t distribution in estimation and hypothesis testing.
This includes sampling theory and the Central Limit Theorem. The construction of confidence intervals for population means and proportions, using the standard normal distribution or the t distribution, as appropriate, and hypothesis tests of a single mean, a single proportion, the difference between two means and the difference between two proportions.
5. Use correlation and regression analysis to identify the strength and form of relationshipsbetween variables.
In correlation analysis, this includes the use of scatter diagrams to illustrate linear association between two variables, Pearson’s coefficient of correlation and Spearman’s ‘rank’ correlation coefficient and the distinction between correlation and causality. In regression analysis, students are expected to be able to estimate the ‘least squares’ regression line for a two variable model and interpret basic results from simple and multiple regression models.
6. Demonstrate how time-series analysis can be used in business forecasting.
This includes the use of the additive and multiplicative models to ’decompose’ time series data, the calculation of trends and cyclical and seasonal patterns, and simple forecasting.
7. Distinguish between parametric and non-parametric methods and use the chisquared statistic in hypothesis testing.
This includes using the chi-squared statistic as a test of independence between two categorical variables and as a test of goodness-of-fit.
8. Show how mathematical relationships can be applied to economic and business problems.
This includes the algebraic and graphical representation of demand and supply functions and the determination of equilibrium price and quantity in a competitive market. It also includes the algebraic and graphical representation of cost, revenue and profit functions, with applications to pricing and output determination (including break-even analysis.)
Throughout, students will be expected to be able to define relevant terms and to interpret all results.
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