PPT-Linear Models Two-Way ANOVA

LM ANOVA 2 2 Example Background Bacteria effect of temperature 10 o C amp 15 o C and relative humidity 20 40 60 80 on growth rate cellsd 120 petri dishes with a growth . e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Methods for Dummies. Isobel Weinberg & Alexandra . Westley. Student’s t-test. Are these two data sets significantly different from one another? . William Sealy Gossett. Are these two distributions different?. Analysis by SAS. Interaction Plot . by Excel. The Design. Type of Crime: Burglary or Swindle. Culture of Defendant: American or Chinese. Sex of Juror: Female or Male. DV: Recommended length of sentence. NR 245. Austin Troy. Based primarily on material accessed from Garson, G. David 2010. . Univariate GLM, ANOVA, and ANCOVA. . Statnotes. : Topics in Multivariate Analysis.. http://faculty.chass.ncsu.edu/garson/PA765/statnote.htm. Analysis of Variation. Math 243 Lecture. R. Pruim. The basic ANOVA situation. Two variables: 1 Categorical, 1 Quantitative. Main Question: Do the (means of) the quantitative variables depend on which group (given by categorical variable) the individual is in?. Hao. Chai. Dereck. . Shen. Skull dataset. 138 skulls from 10 regions. Thickness was measured at 219 locations on each skull. Other variables in dataset:. Age of person (at time of death). Sex of person. models. Jeremy Groom, David Hann, Temesgen Hailemariam. 2012 Western . Mensurationists. ’ Meeting. Newport, OR. How it all came to be…. Proc GLIMMIX. Stand Management Cooperative. Douglas-fir. Improve ORGANON mortality equation?. (a.k.a. Analysis of Variance). 1. Outline:. Testing for a difference. in means. Notation. Sums of squares. Mean. squares. The. F distribution. The. ANOVA table. Part II: multiple. comparisons. Worked example. Analysis of Variance. Let’s say we conduct this experiment: effects of alcohol on memory. Basic Design. Grouping variable . (IV, manipulation) with . 2 or more levels. Continuous dependent/criterion variable. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. Data . Set. Popcorn Oil amt. Batch Yield. plain . little. large 8.2. gourmet little large 8.6. plain . . lots large 10.4. gourmet lots large 9.2. Data . Set. Popcorn Oil amt. Batch Yield. plain . little. large 8.2. gourmet little large 8.6. plain . . lots large 10.4. gourmet lots large 9.2. At its lowest level it is essentially an extension of the logic of . t. -tests to those situations where we wish to . compare the means of three or more samples concurrently.. ANOVA. One-way ANOVA. One IV and one DV. Two-way ANOVA Factor Level Means Study Cells defined b y combinations of t w o or more discrete f actors All o ws ef f ects to be decomposed into main ef f ects and inte r actions Model assumptions remain unchanged