Subjective / Written Questions (25)
1. Define range, mean deviation, quartile deviation, variance and standard deviation. Compare their absolute and relative forms and discuss their suitability for different datasets.
2. Derive the formula for variance from raw observations and explain the effect of a change of origin and scale on variance.
3. Explain the coefficient of variation and discuss why it is useful for comparing the consistency of two series measured in different units.
4. Explain moments about the origin and moments about the mean. Establish the relation between the first four moments about the origin and the central moments.
5. Define skewness and kurtosis and explain how moments are used to describe the shape of a distribution.
6. Explain Pearson's correlation coefficient and derive its basic computational form. State its range and interpretation.
7. Distinguish correlation from regression. Explain the relationship between the two regression coefficients and the correlation coefficient.
8. Derive the normal equations for fitting a straight line by the method of least squares and explain the meaning of its parameters.
9. Explain the correlation ratio and distinguish it from Pearson's product-moment correlation coefficient.
10. Explain intraclass correlation and discuss the situation in which it is appropriate.
11. Define Spearman's rank correlation coefficient. Derive the formula for the case of no tied ranks and explain how ties affect its calculation.
12. Explain the fitting of a nonlinear curve by transformation into a linear form. Illustrate with a suitable model.
13. Explain multiple regression of one variable on two other variables and describe the interpretation of the regression coefficients.
14. Define multiple correlation and partial correlation for three variables. Explain how partial correlation differs conceptually from simple correlation.
15. Explain the relationship among simple, multiple and partial correlation coefficients for three variables.
16. Explain the concepts of consistency, independence and association of attributes in a two-attribute classification.
17. Describe the construction of a fourfold contingency table for two attributes and explain how independence is assessed.
18. Define the coefficient of contingency and explain its interpretation as a measure of association between attributes.
19. Explain the distinction between association and independence of attributes, giving an appropriate statistical interpretation.
20. Discuss the purpose of statistical computing and explain why R is useful for statistical analysis.
21. Explain the roles of R, RStudio and R Commander in a statistical computing workflow.
22. Describe how a data file is created in R and explain the basic structure of a data frame.
23. Explain the procedures for importing and exporting data files in R and mention the importance of preserving variable types.
24. Explain data transformation in R with suitable examples of creating, recoding or modifying variables.
25. Describe how graphical representations of data can be produced in R and explain how the choice of graph depends on the data type.