1. Life after linear regression
A survey of Penn State
applied statistics graduate courses

2. The courses Stat 500: Applied Statistics Stat 501: Regression Methods
Stat 502: Analysis of Variance & Design of Expts
Stat 503: Design of Experiments
Stat 504: Analysis of Discrete Data
Stat 505: Applied Multivariate Statistical Analysis
Stat 506: Sampling Theory and Methods
Stat 509: Biostatistical Methods
Stat 510: Applied Time Series Analysis

3. Stat 500: Applied Statistics
Topics covered:
Descriptive statistics
Hypothesis testing and power
Estimation and confidence intervals
Regression
One- and two-way ANOVA
Chi-square tests
Prerequisites
2 credits of algebra

4. Stat 501: Regression Methods
Topics covered:
Analysis of research data through simple and multiple regression and correlation
Polynomial models
Indicator variables
Stepwise and piecewise regression
Logistic regression
Prerequisites
6 credits of statistics or Stat 500; matrix algebra

5. Stat 502: Analysis of Variance and Design of Experiments
Analysis of data when:
the response y is continuous
the predictors (called factors or treatments) are all qualitative
have same error assumptions as for regression
Do the means differ among the groups defined by the factor combinations?

6. Stat 502: Analysis of Variance and Design of Experiments
Topics covered:
Analysis of variance and design concepts
Factorial, nested and unbalanced data
Analysis of covariance
Blocked designs
Latin-square, split-plot, repeated measures designs
Multiple comparisons
Prerequisites
Stat 501 (or undergraduate version Stat 462)

7. A Stat 502 Example: Intertidal Seaweed Grazers
To study influence of ocean grazers on regeneration rates of seaweed in intertidal zone, a researcher scraped square rock plots free of seaweed and observed the seaweed regeneration when certain types of seaweed-grazing animals were denied access.
Research questions:
Which grazer consumes most seaweed?
Do different grazers influence impact of each other?
Are grazing effects similar in all microhabitats?

8. A Stat 502 Example: Intertidal Seaweed Grazers
The grazers were limpets (L), small fishes (f), and large fishes (F):
LfF: all three grazers were allowed access
fF: limpets were excluded using caustic paint
Lf: large fish were excluded using coarse net
f: limpets and large fish were excluded
L: small, large fish excluded using fine net
C: the control group, all excluded

9. A Stat 502 Example: Intertidal Seaweed Grazers
Intertidal zone is a highly variable environment. Researcher applied treatments in 8 blocks of 12 plots each:
#1: Just below high tide, exposed to heavy surf
#2: Just below high tide, protected from surf
#3: Midtide, exposed
#4: Midtide, protected
#5: Just above low tide level, exposed
#6: Just above low tide level, protected
#7: On near-vertical rock wall, midtide, protected
#8: On near-vertical rock wall, above low tide, protected

10. A Stat 502 Example: Percent of regenerated seaweed on intertidal plots with some grazers excluded
Block
Control L f Lf fF
LfF 1
14, 23
4, 4
11, 24
3, 5
10, 13
1, 2 2
22, 35
7, 8
14, 31
3, 6
10, 15 3
67, 82
28, 58
52, 59
9, 31
44, 50
6, 9 4
94, 95
27, 35
83, 89
21, 57
57, 73
7, 22 5
34, 53
11, 33
33, 34
5, 9
26, 42
5, 6 6
58, 75
16, 31
39, 52
26, 43
38, 42
10, 17 7
19, 47
6, 8
43, 53
4, 12
29, 36
5, 14 8
53, 61
15, 17
30, 37
12, 18
11, 40
5, 7

11. Stat 503: Design of Experiments
The key word is “experiments”
When you can control the values of your predictors (factors), you should ensure you can answer your research question by:
Collecting the appropriate measurements
Setting the values of your factors appropriately
Reducing extraneous variation by “blocking”
Having an appropriate sample size

12. Stat 503: Design of Experiments
Topics covered:
Design principles
Optimality
Confounding in split-plot designs
Repeated measures designs, fractional factorial designs, response surface designs
Balanced/partially balanced incomplete block designs
Prerequisites:
Stat 501 (or undergraduate Stat 462)
Stat 502

13. A Stat 503 Example: The BARGE Study
Current standard treatment for patients with mild to moderate asthma is scheduled daily use of inhaled albuterol.
Now hypothesized that such regular use has a negative effect on lung function in patients with B16Arg/Arg genotype, but not in those with B16Gly/Gly genotype.

14. A Stat 503 Example: The BARGE Study
The BARGE Study concerns comparing the regular use of inhaled albuterol (A) to placebo (P) in patients with the B16Arg/Arg genotype (R) and in patients with the B16GlyGly genotype.
The primary hypothesis concerns inference about whether (μRA- μRP)- (μGA- μGP) is 0.

15. A Stat 503 Example: BARGE Study’s Paired Crossover
Order
Period 1
Washout
Period 2
GenotypeR
1 (AP)
Y1jRA
---
Y1jRP
2 (PA)
Y2jRP
Y2jRA
GenotypeG
Y1jGA
Y1jGP
Y2jGP
Y2jGA

16. Stat 504: Analysis of Discrete Data
Analysis of data when:
the response y is binary or discrete
the predictors are qualitative or quantitative
Summarized data are frequency counts
How do the predictors affect the response?

17. Stat 504: Analysis of Discrete Data
Topics covered:
Models for frequency arrays
Goodness-of-fit tests
Two-, three- and higher-way tables
Latent models
Logistic and Poisson regression models
Prerequisites
Stat 502 (or undergraduate Stat 460 or major Stat 512)
Matrix algebra

18. A Stat 504 Example: Survival in the Donner Party
In 1846, Donner and Reed families traveled from Illinois to California by covered wagon.
Group became stranded in eastern Sierra Nevada mountains when hit by heavy snow.
40 of 87 members (45 adults over age 15) died from famine and exposure.
Are females better able to withstand harsh conditions than are males?

19. A Stat 504 Example: Survival in the Donner Party

20. A Stat 504 Example: Survival in the Donner Party
Link Function: Logit
Response Information
Variable Value Count
STATUS SURVIVED (Event)
DIED
Total
Logistic Regression Table
Odds % CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Constant
AGE
Gender

21. Stat 505: Applied Multivariate Statistical Analysis
Analysis of data when you have several correlated, continuous responses is called multivariate data analysis.
A repeated measure is a special kind of multivariate response obtained by measuring the same variable on each subject several times, possibly under different conditions.

22. Stat 505: Applied Multivariate Statistical Analysis
Topics covered:
Multivariate data: matrix review, graphical displays, probability theory, multivariate normal distribution, partial correlations
Inferences about multivariate means: Hotelling’s T2 tests, multivariate analysis of variance, repeated measures experiments and growth curves, discriminant analysis
Data reduction: Principal components, factor analysis, canonical correlation analysis, cluster analysis
Structural equation modeling
Prerequisites:
6 credits in statistics
Matrix algebra

23. A Stat 505 Example: Pottery Data
Pottery samples were collected from four sites in the British Isles: Llanedyrn, Caldicot, Isle Thornes, and Ashley Rails.
Each piece analyzed for its aluminum, iron, magnesium, calcium, and sodium content.
Do the pottery samples from the four sites differ with respect to their composition?

24. A Stat 505 Example: Pottery Data

25. Stat 506: Sampling Theory and Methods
Topics covered:
Basic methods: simple random sampling, selecting sample sizes, unequal probability sampling, ratio and regression estimation, stratified sampling, cluster and systematic sampling, multistage designs, double sampling
Special topics: sampling hidden human populations, environmental sampling, sampling to study cause-and-effect relationships, resampling of data, measurement errors and nonresponse in surveys, adaptive sampling, network and snowball sampling
Prerequisites:
Calculus
3 credits in statistics

26. A Stat 506 Example: A Water Pollution Survey
Study region of interest has 320 lakes.
Take random sample of the lakes by:
Drawing a rectangle of length l and width w around study region.
Generate pairs of (0,1) random numbers. Multiple first number by l, second by w to get random location coordinates within region.
If location is a lake, then lake is selected.
Continue until required number of lakes selected.

27. Stat 509: Biostatistics Topics covered: Prerequisites:
An introduction to the design and statistical analysis of randomized and observational studies in biomedical research
Prerequisites:
Stat 500

28. Stat 510: Applied Time Series Analysis
Topics covered:
Identification of models for empirical data collected over time
Use of models in forecasting
Prerequisites:
Stat 501 (or undergraduate Stat 462 or major Stat 511)

29. A Stat 510 Example: Measuring Global Warming
Temperature (in degrees Celsius) averaged for the northern hemisphere over a full year.
Temperature series collected from 1880 to 1987.
All measurements expressed as differences from their 108-year mean.
Research questions:
Is the mean temperature increasing over the 88 years?
What is the rate of increase in global temperature over the past century?

30. A Stat 510 Example: Measuring Global Warming

31. A Stat 510 Example: Measuring Global Warming