I. Introduction to the course
(Class 1)
A. Who should take the class
B. The textbook and class logistics
C. Topics to be covered during the semester
D. Introduction to WebCT & CENTRA
E. Brief introduction to SPSS on the PC
II. Chapter 1 Drawing statistical conclusions (1)
(Class 2)
A. Case studies
- Motivation and Creativity
- Sex discrimination in employment
B. Statistical inference and study design
C. Measuring uncertainty in randomized experiments
D. Measuring uncertainty in observational studies
E. Related issues
F. Summary
III. Chapter 2 Inference using t-distributions (28)
(Class 3-4)
A. Case studies
- Bumpus’s Data on Natural Selection — An observational study
- Anatomical abnormalities associated with schizophrenia — An observational study
B. One-sample t-tools and the paired t-test
- The sampling distribution of a sample average
- The standard error of an average
- The t-ratio based on a sample average
- Unraveling the t ratio
C. A t-ratio for two sample inference
- Sampling distribution of the difference between tow independent sample averages
- Standard error for the difference of two averages
D. Inferences in a two-treatment randomized experiment
E. Related issues
F. Summary
G. Exercises
IV. Chapter 3 A closer look at assumptions (56)
(Class 5)
A. Case studies - Cloud seeding to increase rainfall – A randomized experiment
- Effects of Agent Orange on troops in Viet Nam – An observational study
B. Robustness of two sample t-tools C. Resistance of the two sample t-tools D. Practical strategies for the two sample problem E. Transformations of the data - The Logarithmic Transformation
- Interpretation after a Log Transformation
- Other Transformations for Positive Measurements
F. Related issues G. Summary H. Exercises
- V.Chapter 4 Alternatives to the t-tools (85) (Class 6)
A. Case studies
1. Space shuttle O-Ring Failures – An observational study
2. Cognitive Load Theory in Teaching – A Randomized Experiment
B. The rank-sum test
- The Rank Transformation
- The Rank-sum statistic
- Finding a p-value by normal approximation
- A confidence interval based on the rank-sum test
C. Other alternatives for two independent samples
- Permutation tests
- The Welch t-test for comparing two normal populations with unequal spreads
D. Alternatives for paired data
- The Sign test
- The Wilcoxon Signed Rank Test
E. Related issues
- Practical and Statistical Significance
- The Presentation of Statistical Findings
- Levene’s test for Equality of two variances
- Survey sampling
F. Summary
G. Exercises
VI. Chapter 5 Comparisons among several samples (113)
(Class 7-9)
A. Case studies
- Diet restriction and longevity
- Benjamin Spock conspiracy trial
B. Comparing any two of the several means
- An ideal model
- The pooled standard deviation
- t-tests and confidence limits for differences of means
C. The one-way analysis of variance F-test
- The extra sum of squares principle
- the ANOVA table
- More applications of the extra sum of squares principle
D. Robustness and model checking
- Robustness to assumptions
- Diagnostics using residuals
E. Related issues
- Further illustrations of different sources of variability
- Kruskal-Wallis nonparametric ANOVA
- Random effects
- Separate confidence intervals and significant differences.
F. Summary
G. Exercises
1. Ex 5.23 T. rex temperature
VII. Chapter 6 Linear combinations and multiple comparisons of means (149)
(Class 9 &
10)
A. Case studies
- Discrimination against the handicapped
- Sexual selection in swordtails
B. Inferences about linear combinations of group means
C. Simultaneous inferences
D. Some multiple comparison procedures
E. Related issues
F. Summary
G. Exercises
VIII. Chapter 7 Simple linear regression: a model for the Mean (174)
(Class 11)
A. Case studies
- The Big Bang
- Meat Processing and pH
B. The simple linear regression model
C. Least squares regression estimation
D. Inferential tools
- Tests and confidence limits for slope and intercept
- Describing the distribution of the response at some value of explanatory variable
- Prediction of a future response
- Calibration: Estimating the X that results in Y=Y {See also Draper &
Smith 1998, Chapter 3 }
E. Related issues
F. Summary
G. Exercises
IX. Chapter 8 A Closer look at assumptions for simple linear regression
(206) (Class 12-14)
A. Case studies
- Island area and number of species – an observational study
- Breakdown times for insulating fluid under different voltages – a controlled experiment
B. Robustness of least-squares inferences
C. Graphical tools for model assessment
D. Interpretation after log transformations
E. Assessment of fit using the analysis of variance
F. Related issues
G. Summary
H. Exercises
X. Chapter 9 Multiple Regression (235) (Class 14)
A. Case studies
- Effect of light on meadowfoam flowering – a randomized experiment
- Why do some mammals have large brains for their size – an observational study
B. Regression coefficients
- The multiple linear regression model
- Interpretation of regression coefficients
C. Specially constructed explanatory variables
- A squared term for curvature
- An indicator variable to distinguish between two groups
- Sets of indicator variables for categorical explanatory variables with more than two categories
- A product term for interaction
- A shorthand notation for model description
D. A strategy for data analysis
E. Graphical methods for data exploration and presentation
F. Related issues
G. Summary
H. Exercises
XI. Midterm Exam (3/22/06 W)
(Class 15)
XII. Chapter 10 Inferential tools for multiple regression (267) ( Class 16)
A. Case studies
- Galileo’s data on the motion of falling bodies – a controlled experiment
- The Energy costs of echolocation by bats – an observational study.
B. Inferences about regression coefficients
- Least squares estimates and standard errors
- Tests and confidence intervals for single coefficients
- Tests for confidence limits for linear combinations of coefficients
- Prediction
C. Extra-sum-of-squares F tests
D. Related issues
E. Summary
F. Exercises
XIII. Chapter 11 Model checking and refinement (304)
(Class 17)
A. Case studies
- Alcohol metabolism in men and women – an observational study
- The blood-brain barrier – a controlled experiment
B. Residual plots
C. A strategy for dealing with influential observations
- Assessment of whether observations are influential
- What to do with influential observations
D. Case-influenced statistics
- Leverages for flagging cases with unusual explanatory variable values
- Studentized residuals for flagging outliers
- Cook’s distances for flagging influential cases
- A strategy for using case influence statistics
E. Refining the model
- Testing terms
- Partial residual plots
F. Related Issues
- Weighted regression for certain types of non-constant variance
- Measurement errors in explanatory variables
G. Summary
H. Exercises
XIV. Chapter 12 Strategies for variable selection (338)
(Class 18-19)
A. Case Studies
- State average SAT scores – an observational study
- Sex discrimination in employment – an observational study
B. Specific issues relating to many explanatory variables
- Objectives
- Loss of precision
- A strategy for dealing with many explanatory variables
C. Sequential variable selection techniques
- Forward selection
- Backward elimination
- Stepwise regression
- Sequential variable selection with the SAT data
- Compounded uncertainty in stepwise procedures
D. Model selection among all subsets
E. Analysis of the Sex discrimination data
F. Related issues
G. Summary
H. Exercises
XV. Chapter 13 The Analysis of Variance for Two-way classifications (374) (Class 20-21)
A. Case studies
- Intertidal seaweed grazers – A randomized experiment
- The Pygmalion effect in training programs – A randomized experiment
B. Additive and nonadditive models for two-way tables
- The Additive Model A Regression Parameterization for the additive two-way model
- The Saturated, nonadditive model
- A strategy for analyzing two-way tables with several observations per cell.
- The analysis of variance F-test for additivity
C. Analysis of the seaweed grazer data
- Initial assessment of additivity, outliers and the need for transformation
- The analysis of variance table from the fit to the saturated model
- The analysis of variance table for the fit to the additive model
- Answers to specific questions of interest using contrasts
- Answers to specific questions of interest using multiple regression with indicator variables
D. Analysis of the Pygmalion data
- Initial Exploration and check on the additive model
- Answering the question of interest with regression
- A closer look at the regression estimate of treatment effect
- The p-value in the randomization distribution
E. Related Issues
- Additivity and nonadditivities
- Orthogonal contrasts
- Randomized blocks and paired-t analyses
- Should insignificant block effects be eliminated from the model?
- Multiple comparisons
- An alternate parameterization for the additive model
F. Summary
G. Exercises
XVI. Chapter 14 Multifactor studies without replication (409)
(Class 22)
A. Case Studies
- Chimpanzees Learning Sign language – a controlled experiment Fouts (1973)
- Effects of ozone in conjunction with sulfur dioxide and water stress on soybean yield – a randomization experiment
B. Strategies for analyzing tables with one observation per cell
C. Analysis of the Chimpanzee learning times study
D. Analysis of the soybean data
E. Related issues
1. Nested ANOVA
F. Summary
G. Exercises
XVII. Chapter 15 Adjustment for serial correlation (436) (Class 23)
A. Case Studies
- Logging practices and water quality – an observational study
- Measuring global warming – an observational study
B. Comparing the means of two time series
- Serial correlation and its effect on the average of a time series
- The standard error of an average in a serially correlated time series
- The first serial correlation coefficient
- Pooling estimates and comparing means of two independent time series with the same first serial correlation
C. Regression after Transformation in the AR(1) model
- The serial correlation coefficient based on regression residuals
- Regression with filtered variables
D. Determining if serial correlation is present
- An easy large-sample test for serial correlation
- The nonparametric runs test
- The Durbin-Watson test statistic
E. Diagnostic procedures for judging the adequacy of the AR(1) model
- When is a transformation of a time series indicated
- The partial autocorrelation function (PACF)
- Bayesian information criterion
F. Related Issues
G. Summary
H. Exercises
XVIII. Chapter 16 Repeated Measures (462) (Class 24)
A. Case Studies
- Sites of short- and long-term memory — A controlled experiment
- Oat Bran and cholesterol — A randomized crossover experiment
B. Tools and strategies for analyzing repeated measures
- Types of repeated measures studies
- Profile plots for graphical exploration
- Strategies for analyzing repeated measures
C. Comparing the means for bivariate responses in two groups
- Summary statistics for bivariate responses
- Pooled variability estimates
- Hotelling’s T^{2 } statistic.
- Checking on assumptions
- Confidence ellipses
D. Related Issues
E. Summary
F. Exercises
XIX. Chapter 17 Exploratory tools for summarizing multivariate responses (497) (Class 25)
A. Case studies
- Magnetic force on rods in printers
- Love and Marriage — an observational study
B. Linear combinations of variables
C. Principal components analysis
- The PCA train
- Principal components
- Variables suggested by PCA
- Scatterplots in PCA space
- The factor analysis model and PCA
- PCA usage
D. Canonical correlation analysis
E. Introduction to other multivariate tools
- Discriminant function analysis
- Multidimensional scaling
- Correspondence analysis
- PCA and Empirical Orthogonal Functions (EOFs)
F. Summary
G. Exercises
XX. Chapter 18 Comparisons of proportions or odds (529)
A. Case Studies
- Obesity and heart disease in American Samoa
- Vitamin C and the common cold
B. Inferences for the difference of two proportions
C. Inference about the ratio of two odds
D. Inference from retrospective studies
E. Summary
F. Exercises
XXI. Chapter 19 More tools for tables of counts (552)
A. Case studies
- Sex role stereotypes and personnel decisions – a randomized experiment
- Death penalty and race of murder victim – an observational study
B. Population models for 2 x2 tables of counts
- Hypotheses of homogeneity and independence
- Sampling schemes leading to 2 x 2 tables
- Testable hypotheses and estimable parameters
C. The ÷-squared test
- The Pearson ÷-squared test for Goodness of Fit
- ×-squared test of independence in a 2 x 2 table
- Equivalence of several tests for 2 x 2 tables
D. Fisher’s exact test: the randomization (permutation) test for 2 x 2 tables
- The randomization distribution of the difference in sample proportions
- The hypergeometric formula for one-sided P-values
- Fisher’s exact test for observational studies
- Fisher’s exact test versus other tests
E. Combining results from several tables with equal odds ratios
- The Mantel-Haenszel Excess
- The Mantel-Haenszel test for equal odds in several 2 x 2 tables
- Estimate of the common odds ratio
F. Related issues
- r x c tables of counts
- Higher dimensional tables of counts
- Analysis of SUV fatalities & the Ford Explorer (new problem)
G. Summary
H. Exercises
XXII. Chapter 20 Logistic regression for binary response variables (579)
A. Case studies
- Survival in the Donner Party – An observational study
- Birdkeeping and lung cancer – A retrospective observational study
B. The logistic regression model
C. Estimation of the logistic regression coefficients
D. the Drop-in-deviance test
E. Strategies for data analysis using logistic regression
F. Analysis of case studies
G. Related issues
H. Summary
I. Exercises
XXIII. Chapter 21 Logistic regression for binomial counts (609)
A. Case studies
- Island size and bird extinctions – an observational study
- Moth coloration and natural selection – A randomized experiment
B. Logistic regression for binomial responses
C. Model assessment
D. Inferences about logistic regression coefficients
E. Extra-binomial variation
F. Analysis of moth predation data
G. Related issues
H. Summary
I. Exercises
XXIV. Chapter 23 Elements of Research design (669)
A. Case study Biological control of a noxious weed – a randomized experiment
B. Considerations for forming research objectives
C. Research design tool kit
- Controls and placebos
- Blinding
- Blocking
- Stratification
- Covariates
- Randomization
- Random sampling
- Replication
- Balance
D. Design choices that affect accuracy and prediction
- Attaching desired precision to practical significance
- How to improve a confidence interval
E. Choosing a sample size
- Studies with a numerical response
- Studies comparing two proportions.
- Sample size for estimating a regression coefficient
F. Steps in designing a study
- Stating the objective
- Determining the scope of inference
- What experimental units will be used?
- What are the populations of interest
- Understanding the system
- Deciding how to measure a response
- Listing factors that can affect the response
- Planning the conduct of the experiment
- Outlining the statistical analysis
- Determining the sample size
G. Related issues – a factor of four
H. Summary
I. Exercises
XXV. Chapter 24 Factorial treatment arrangements and blocking designs
A. Case study
1. Amphibian crisis linked to ultraviolet – a randomized experiment
B. Treatments
- Choosing treatment levels
- The rationale for several factors
C. Factorial arrangement of treatment levels
1.Definition and terminology for a factorial arrangement
2.The 2^2 factorial structure
3.The 2^3 factorial structure
4.The 3^2 factorial structure
5.Higher order factorial arrangements
D. Blocking
- Randomized blocks
- Latin square blocking
- Split Plot designs
E. Summary
F. Exercises
XXVI. Chapter 22 Log-linear regression for Poisson counts
A. Case studies
- Age and elephant mating success
- Treatment for epileptic seizures
B. Log-linear regression for Poisson responses
C. Model assessment
D. Inferences about log-linear regression coefficients
E. Extra-Poisson variation and the log-linear model
F. Further issues
G. Summary
H. Exercises