Life after linear regressionThe coursesStat 500: Applied StatisticsStat 501: Regression MethodsStat 502: Analysis of Variance and Design of ExperimentsSlide 6A Stat 502 Example: Intertidal Seaweed GrazersSlide 8Slide 9A Stat 502 Example: Percent of regenerated seaweed on intertidal plots with some grazers excludedStat 503: Design of ExperimentsSlide 12A Stat 503 Example: The BARGE StudySlide 14A Stat 503 Example: BARGE Study’s Paired CrossoverStat 504: Analysis of Discrete DataSlide 17A Stat 504 Example: Survival in the Donner PartyA Stat 504 Example: Survival in the Donner PartySlide 20Stat 505: Applied Multivariate Statistical AnalysisStat 505: Applied Multivariate Statistical AnalysisA Stat 505 Example: Pottery DataA Stat 505 Example: Pottery DataStat 506: Sampling Theory and MethodsA Stat 506 Example: A Water Pollution SurveyStat 509: BiostatisticsStat 510: Applied Time Series AnalysisA Stat 510 Example: Measuring Global WarmingSlide 30Slide 31Life after linear regression A survey of Penn State applied statistics graduate coursesThe 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 AnalysisStat 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 algebraStat 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 algebraStat 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?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)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?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 excludedA 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, protectedA Stat 502 Example:Percent of regenerated seaweed on intertidal plots with some grazers excludedBlock Control L f Lf fF LfF1 14, 23 4, 4 11, 24 3, 5 10, 13 1, 22 22, 35 7, 8 14, 31 3, 6 10, 15 3, 53 67, 82 28, 58 52, 59 9, 31 44, 50 6, 94 94, 95 27, 35 83, 89 21, 57 57, 73 7, 225 34, 53 11, 33 33, 34 5, 9 26, 42 5, 66 58, 75 16, 31 39, 52 26, 43 38, 42 10, 177 19, 47 6, 8 43, 53 4, 12 29, 36 5, 148 53, 61 15, 17 30, 37 12, 18 11, 40 5, 7Stat 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 sizeStat 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 502A 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.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.A Stat 503 Example:BARGE Study’s Paired CrossoverOrderPeriod 1WashoutPeriod 2GenotypeR1 (AP)Y1jRA---Y1jRP2 (PA)Y2jRP---Y2jRAGenotypeG1 (AP)Y1jGA---Y1jGP2 (PA)Y2jGP---Y2jGAStat 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?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 algebraA Stat 504 Example:Survival in the Donner Party •In 1846, Donner and Reed families traveled from Illinois
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