# THEORY OF STATISTICS PART I

A course of three lectures per week, with demonstrations, tutorial and practice classes, throughout the year.

5уLLAВus. Introduction to the theory of probability; finite event space;

simple and compound events ; intersection and union ; assigning of probabilities to events ; conditional probability ; independence of events ; problems involving theory of arrangements ; infinite discrete and continuous event spaces. Random variables;

probability distributions ; cumulative distribution function and probability density function; parameters associated with distributions. Standard elementary univariate distributions (discrete rectangular, binomial, negative binomial, hyPergeometric, Poisson, uniform, normal). Treatment of experimental data; sample and popu- lation ; notion of decision rules for preferring one model to another. Acceptance sampling plans ; quality control technique. Exact treatment of 2 X 2 classifications for independence (binomial case). Distribution of sample statistics (arithmetic mean, sample variance and standard deviation, range, etc.). The t, F and chi-square.

distributions. Model building and testing ; confidence intervals for parameters.

Difference of proportions. Application of chi-square distribution to testing of hypotheses. Principles of experimental design and the analysis of variance tech- nique; standard designs, one-way (completely randomized), two-way (randomized

blocks) and Latin square lay-outs, and extensions; factorial design; confounding in simple cases ; description of split-plot and incomplete block designs. Bivariate distributions ; the normal bivariate distribution ; linear regression and correlation with two and three variables ; method of last squares ; analysis of covariance technique.

PRACTICAL WORK. Three hours per week, on problems and computations relating to the lecture course and involving the use of calculating machines, hand- operated and electric.

A knowledge of mathematics up to the standard of Pure Mathematics Part I will be assumed in the above course.

Boors. (a) Prescribed tables:

*Lindley, D. V., and Miller, J. C.

### P.—Caimbridge .• Elementary Statistical Tables.

(C.U.P.)

(b) Recommended for reference:

bel, P.

### G.—Introduction to Mathematical Statistics.

(2nd ed., (`hapman &

Hall, 1954.) (This book is specially recommended.)

Davies, O.

(Oliver &

Boyd,)

Snedecor, G.

### W.—Statistical Methods.

(Collegiate Press, Ohio.) Fisher; R. A., and Yates,

### F.—Statistical Tables.

(Oliver & Boyd.) Wilks, S.

### S.—Elementary Statistical Analysis.

(Princeton U.P.)

EXAMINATION. Two 3-hour papers. Before admission to the examination, candidates must have satisfactorily completed the practical work.

THEORY OF STATISTICS PART II

A course of three lectures per week, with demonstrations, tutorial and practice classes, throughout the year.

SУLLAВus. Discrete and continuous probability distributions; transformation of variables in univariate and multivariate cases. Characteristic function. Deri- vation . of the common sampling distributions. Theories of point and interval estimation. Theory of significance tests. Sequential analysis. Distribution-free methods. Probability theory. Regression analysis and linear hypotheses, with detailed application in the design and analysis of experiments.

PRACTICAL Woкк. Six hours per week, including computations involving the use of calculating machines.

A knowledge of mathematics up to the standard of Pure Mathematics Part II will be assumed in the above course. In addition, students will find it an advantage to be currently taking the course in Pure Mathematics Part III.

Candidates may be required to read original papers dealing with certain aspects

of the course. ,

Boокs. (a) Prescribed text-books :

*Cochran, W. G., and Cox, G. М.—Experimental Designs. (Wiley.)

*Mood, А. M. Introduction to the Theory of Statistics. (McGraw-Hill.) (b) Recommended for reference:

Aitken, A.

(Oliver & Boyd.)

Davies, O.

### L. Design and Analysis of Industrial

Experiments. • (Oliver &

Boyd.)

Anderson, R. L., and Bancroft, T.

(Mc- Graw-Hill.)

Kendall, M.

### G. The Advanced Theory of Statistics, Vols. I, II.

(Griffin.) Wilks, S.

### S —Mathematical Statistics.

(Princeton U.P.)

Weatherburn, C. E.-A

### First Course in Mathematical Statistics.

(C.U.P.) Fisher, R.

### A.—Statistical Methods for Research Workers.

(Oliver & Boyd.) Fisher, R.

### A: The Design of Experiments.

(Oliver & Boyd.)

Arley, N., and Buch, K.

(Wiley.)

Neyman,

### J.

—A First Course in Probability and Statistics. (Holt.) 121

Johnson, N. L., and Tetley, H.—Statistics: An Intermediate Text-book, Vols.

I, II. (C.U.P.)

Feller, W. An Introduction to Probability Theory and its Applications, Vol.

I. (Wiley.)

Fisher, R. A., and Yates, F. Statistical. Tables. (Oliver & Boyd.)

Pearson, E. S. and Hartley, Н. O. Вiometrika Tables for Statisticians, Vol.

I. (C.U.P.)

ExAMINATiox. Two 3-hour papers and a practical test. Before admission to the examination, candidates must have satisfactorily completed the practical work.

### (b) PSYCHOLOGY PSYCHOLOGY PART I

A course of two lectures with one tutorial class and one laboratory- period of two hours• per week throughout the year. No extra classes will be held for Honour candidates.

### No

correspondence courses are given.

SYLLABUS. The course is designed to be a general introduction to psychology, with particular emphasis on method. Origin and development of behavioural patterns, motivation, emotion, perception, learning. The nature and development of personality. Elementary physiology of the central and peripheral nervous system. Elements of measurement in psychology.

Воoкs. (a) Recommended for preliminary reading:

Collins, M., and Dreyer, J. Psychology and Practical Life. (Univ. of Lind.

Press.)

Cattell, R. B.—Your Mind and Mine. (Harrap.)

Harrower, M. R.—The Psychologist at Work. (Kegan Paul.)

Johns, R. L.—Psychology in Everyday Living. (Harper, 1950.) - (b) Prescribed text-books:

*Munn, N. L-Psychology. (2nd ed., Houghton Mifflin, 1951.) or *Stagner, R., and Karwoski, T. F. Psychology. (McGraw-Hill, 1952.) or *Woodworth, R. S., and Marquis, D. G.—Psychology. (20th ed., Methuen, 1949.)

*Dreyer, J. A Dictionary of Psychology. (Penguin, 1952.)

*Townsend, J. O. Introduction to Experimental Method. (McGraw-Hill, 1953.)

*Department of Psychology—Psychometrics—Psychology Part I. (Rev. ed., Melb. U.P., 1955.)

Walker, H. 1.—Elementary Statistical Methods. (Holt, 1943.) (c) Recommended for reference: -

Boring, E. G., Langfeld, H. S., and Weld, H. P. Foundations of Psychology.

(Wiley, 1948.) -

Crafts, L. W., Schneirlа, T. C., Robinson, E. E., and Gilbert, R. W.—Recent Experiments in Psychology. (2nd ed., McGraw-Hill, 1950.)

Eysenck, H. J.—Uses and Abuses of Psychology. (Pelican, 1953.)

Garrett, H. E.—Great Experiments in Psychology. (Rev. ed., Appleton- Century, 1941.)

Katz, D.—Animals and Men. (Pelican, 1953.)

Morgan, C. L., and Stellar, E. Physiological Psychology. (2nd ed., McGraw- Hill, 1950.)

Newcomb, T. M. Social Psychology. (Dryden, 1950.) - - Stafford-Clark, D.—Psychiatry Today. (Pelican, 1952.)

Swanson, G. E., Newcomb, T., and Hartley, E. L.—Readings in Social Psychology. (Rev. ed., Holt, 1952.)

Books recommended for additional reading and reference are listed in the General Manual of the Department of Psychology.

EXAMINATION. Two 3-hour papers. Candidates must submit satisfactory laboratory notebooks. Honour candidates will be required to show in both.

laboratory notebooks and examination papers a wider and more detailed know- ledge than Pass candidates.

Outline

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