AMS 572, Data Analysis I
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).
3 credits, ABCF grading
Department Consent Required
Text:
"Statistics and Data Analysis", by Tamhane and Dunlop, Pearson, 1999, 2nd edition,
Pearson; ISBN: 9780137444267 (required)
"Applied Statistics and SAS Programming Language", by Jeffrey K. Smith, 2005, 5th
edition, Pearson; ISBN: 9780131465329 (recommended)
Offered in Fall Semester
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, for classes beginning Fall 2014) 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).