AMS 572: Data Analysis

Introduction to basic statistical procedures. Survey of elementary statistical procedures such as the t-test and chi-square test. Procedures to verify that assumptions are satisfied. Extensions of simple procedures to more complex situations and introduction to one-way analysis of variance. Basic exploratory data analysis procedures (stem and leaf plots, straightening regression lines, and techniques to establish equal variance).

Required Textbook: Statistics and Data Analysis: From Elementary to Intermediate by Ajit C. Tamhane and Dorothy D. Dunlop, 1999, Pearson

Supplementary Textbook: Applied Statistics and the SAS^® Programming Language by Ronald P. Cody and Jeffrey K. Smith, 5th edition, 2005, Pearson

Learning Outcomes

1. Master the sampling distributions of statistics especially:
   • Sampling from the normal populations;
   • Sampling from the Bernoulli populations;
   • Large sample distribution of sample mean;
   • Distribution of order statistics.
2. Master the basic concepts of statistical inference:
   • Point estimators;
   • Pivotal quantity;
   • Maximum likelihood based methods;
   • Confidence intervals;
   • Hypothesis testing.
3. Demonstrate skills for inference with one population mean (including derivation of the formulas using the pivotal quantity method):
   • Inference on one population mean when the population is normal and the population variance is known;
   • Inference on one population mean when the population is normal and the population variance is unknown;
   • Inference on one population mean when the population distribution is unknown but the sample size is large;
   • Normality test using the normal probability plot and the Shapiro-Wilk test.
4. Demonstrate skills for inference with one population variance when the population is normal (including derivation of the formulas using the pivotal quantity method).
5. Demonstrate skills for inference with two population means (including derivation of the formulas using the pivotal quantity method):
   • Inference on two population means with paired samples – how to reduce that to inference on one population mean with the paired differences;
   • Inference on two population means, two independent samples, when both populations are normal and the population variances are known;
   • Inference on two population means, two independent samples, when both populations are normal and the population variances are unknown but equal;
   • Inference on two population means, two independent samples, when at least one population distribution is not normal but both sample sizes are large.
6. Demonstrate skills for inference with two population variances when both populations are normal (including derivation of the formulas using the pivotal quantity method) – especially the F-test for the equality of two population variances.
7. Master the basic inference with proportions and count data (including derivation of the formulas using the pivotal quantity method for the inference on one-population proportion and two-population proportions):
   • Inference on one population proportion – exact test and large sample inference;
   • Inference on two population proportions, independent samples – exact test and large sample inference;
   • Inference on two population proportions, paired samples – exact test;
   • Inference with one-way contingency table, including the Chi-square goodness-of-fit test;
   • Inference with two-way contingency table, test for homogeneity and test for independence.
8. Master the basic inference with simple linear regression and correlation:
   • Least squares method;
   • Error in variable regression;
   • Bivariate normal distribution;
   • Pearson correlation;
   • Spearman rank correlation.
9. Demonstrate skills with inference on several population means, independent samples – One-Way ANOVA:
   • Understanding of the assumptions, derivation, interpretation of results from statistical analysis;
   • Post-hoc (pairwise) comparison of the population means.
10. Master the related SAS^® and R procedures for all materials covered in lectures.
11. Group presentations covering some of the materials in both text books not covered in the regular lectures including:
    • Multiple regression;
    • One-way ANCOVA;
    • Two-way ANOVA & ANCOVA;
    • Repeated measures ANOVA;
    • Nonparametric methods: Rank based methods;
    • Nonparametric methods: Permutation based (permutation test, Jackknife, Bootstrap).