Statistical Methods
Qualifying Examination Syllabus

Probability Distributions:
Standard distributions such as normal, binomial, hypergeometric, Poisson, gamma, multinomial, multivariate normal; sampling distributions of statistics, t, F, chi-squared, order statistics; basic limit theorems such as law of large numbers and central limit theorem

Basic Statistical Inference:
Tests of hypotheses in one-parameter probability models; standard methods of point and interval estimation for one-parameter probability models.

Analysis of Variance:
One-factor & Two-factor Analysis of Variance models: hypothesis testing (t-test) and F-test); multiple comparisons by Bonferroni's method; estimation and hypothesis testing of linear contrasts.

Linear Regression Analysis:
Linear regression models; ordinary and weighted least squares; simple and multiple regressions; inferences in regression analysis (t-test, F-test, confidence and prediction intervals); residuals analysis; F-test for lack of fit; coefficient of determination; partial correlations; Gauss-Markov theorem; tests for normality.

Nonparametric Methods:
Wilcoxon-Mann-Whitney tests (both one and two sample problems); Empirical distributions; goodness-of-fit tests; categorical data analysis; chi-squared tests; Kolmogorov and Kolmogorov-Smirnov statistics.

Most of the material above can be found in

  • Bickel, P.J. and Doksum, K.A., Mathematical Statistics: Basic Ideas and Selected Topics
  • (a) Draper N. and Smith H., Applied Regression Analysis or
    (b) Neter J., Wasserman W. and Kutner, M.H., Applied Linear Regression Models
  • (a) Hollander M. and Wolfe, D.A., Nonparametric Statistical Methods or
    (b) Lehmann, E.L., Nonparametrics: Statistical Methods Based on Ranks
  • Rice, John, Mathematical Statistics and Data Analysis
  • Lecture Notes from Math 231, Math 309, Math 312, Math 334, Math 338, Math 461 and Math 462