San Jose State University

Department of Mathematics

Math 161B

Applied Statistics II

Catalog Description

A continuation of Applied Statistics I, Math 161A. Analysis of variance for one-factor and multi-factor experiments. Linear and multiple regression. Use of statistical software in the computer lab is an integral part of the course. Student project required.

Prerequisite

Math 161A (Applied Statistics I) with a grade of C- or better.

Textbooks

Jay Devore, Probability and Statistics for Engineering and the Sciences, 7th ed., Duxbury, 2008.

Other suitable texts

Navidi, (2007). Statistics for Engineers and Scientists, 2nd edition, McGraw-Hill.

Walpole, Meyers, Meyers, and Ye, (2006). Probability and Statistics for Engineers and Scientists, 8th edition, Prentice Hall.

Levine, Ramsey, Smidt, (2000) Applied Statistics for Engineers and Scientists: Using Microsoft Excel and Minitab, Prentice Hall.

Hogg & Ledolter, (1992). Applied Statistics for Engineers and Physical Scientists, 2nd. edition, Macmillan.

References

none

Technology Requirement

The use of statistical software is required for data analysis. Possible software packages include SPSS, Minitab, JMP and/or R. The software should be chosen with availability in mind. Does SJSU currently hold a student license? A scientific calculator which has an exponential key (yx) and a factorial key (x!) is needed for some of the homework assignments as well as for the exams. A graphing calculator, such as the TI-82, or TI-85, is useful but is not required.

Course Content

Review of hypothesis testing from Applied Statistics I, Math 161A. Introduction of two-sample tests. Analysis of variance for one-factor and several-factor experiments. Linear and multiple regression. Use of statistical software is an integral part of the course. The students should work on a (data analysis) project using the methods discussed in the course.


Topics

The chapters and topics listed all correspond to those in the Devore text.

Ch. 7&8. Confidence Intervals and Hypothesis Testing – Review only

All of this material should already be known to Math 161A students:

7  Basic concept of a confidence interval: z- and t-confidence intervals for means and proportions of one population. Interpretation of confidence.

8  Review of basic concept of a hypothesis test: null and alternative hypothesis, test statistics, critical region(s), type I and type II errors, p-values.

Ch. 9. Inferences Based on Two Samples.

9.1 z-test and confidence interval for comparing two population means

9.2 t-test and confidence interval for comparing two population means

9.3 Analysis of paired data

9.4 Tests and confidence intervals for differences in population proportions

Ch. 10. Analysis of Variance (one factor)

10.1. Analysis of variance for completely randomized one-factor experiments: the error sum of squares and the mean square due to error, the treatment sum of squares and the mean square due to treatment, the ANOVA (analysis-of-variance) table, the F-test for treatment effects. The alternative Anova model.

10.2 Multiple Comparisons in Anova. Tukey’s procedure

10.3. Unequal sample sizes. Random effects model.

Ch. 11. Multifactor Analysis of Variance

11.1. Two-factor Anova without replication. Additive model. Anova table, sums of squares. F-test. Model assumptions. Randomized Block design.

11.2 Two-factor Anova model with interaction. Testing procedures. Multiple comparisons.

11.3 Three-factor Anova. Latin Square designs. Fixed and Random effects.

11.4 Factorial Experiments.

Ch. 12&13. Regression Analysis

12.1. The simple linear regression model.

12.2. Estimating model parameters, the least squares idea. Predicted values. Correlation and the coefficient of determination.

12.3. Inferences about the model parameters. The Anova table for regression. Hypothesis tests about the intercept and slope. Inference for predicted values. Inference on correlation.

13.1. Model checking. Residual analysis. Diagnostic plots and their interpretation.

13.2. Variable transformations. Logistic regression.

13.3. Polynomial regression.


Ch. 13. Multiple Regression Analysis

13.4. The general additive multiple regression model. Categorical predictors, dummy variables. Parameter estimation. The model utility test. Interaction.

13.5. Variable selection. Multicollinearity. Diagnostics.

Ch. 14. Categorical Data Analysis

14.1 Goodness-of-fit test

14.2 Two-way contingency tables. c2-test for homogeneity and independence.

Special Topics (optional):

Non-parametric procedures

Permutation tests

Bootstrap

Topics and Suggested Course Schedule

The chapters and topics listed below correspond to those in the Devore text.

Topic / Number of 75-minute lectures
Ch. 7&8: Review of Hypothesis Testing and Confidence Intervals / 2
Ch. 9: Two-Sample Tests / 2
Ch.10: Analysis of Variance (ANOVA) for Experiments with One Factor. / 2
Ch. 11: Analysis of Variance for Experiments with Two or More Factors. / 6
Ch. 12: Simple Linear Regression / 5
Ch. 13: Multiple Regression / 5
Ch. 14: Categorical Data Analysis / 3
Additional Topics / 2.5
Student project presentations / 1.5
Exams / 2
TOTAL / 31

Prepared by:

Martina Bremer

Probability and Statistics Committee

Department of Mathematics, SJSU

March 30th, 2009