PPT-Regression Part II One-factor ANOVA

Another dummy variable coding scheme Contrasts Multiple comparisons Interactions One factor Analysis of variance Categorical Explanatory variable Quantitative Response variable p categories groups. AMS 572 Group 5. Outline. Jia. Chen: Introduction of repeated measures ANOVA. Chewei. Lu: One-way repeated measures . Wei Xi: Two-factor repeated measures. Tomoaki. Sakamoto : Three-factor repeated measures. 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?. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. 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. (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. Example Data Set. Y. X. 5. 20. 6. 23. 7. 27. 8. 33. 8. 31. 9. 35. 10. 43. 5. 19. 6. 25. 7. 29. 8. 31. Estimate two models. Model with y-intercept. Y = a b * X. Regression Statistics. Multiple R. 0.984. Department of Applied Mathematics & Statistics. Stony Brook University. Review of . (the non-repeated measures) . ANOVA. 2. Review of ANOVA. The One-way ANOVA we have just learnt can test the equality of several population means.. 1. Data on pain and factor levels. male C 12.4. female A 7.69. male C 14.0. female A 9.69. male C 11.6. female A 8.89. female A 6.94. female A 2.13. female A 7.26. female A 5.87. male B 12.9. female C 12.2. 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. In linear regression, the assumed function is linear in the coefficients, for example, . .. Regression is nonlinear, when the function is a nonlinear in the coefficients (not x), e.g., . T. he most common use of nonlinear regression is for finding physical constants given measurements.. ANOVA is comparison of means. Each possible value of a factor or combination of factor is a treatment.. The ANOVA is a powerful and common statistical procedure in the social sciences. It can handle a variety of situations..