PPT-t -tests, ANOVA & Regression

Andrea Banino amp Punit Shah Samples vs Populations Descriptive vs Inferential William Sealy Gosset Student Distributions probabilities and Pvalues Assumptions of ttests. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. 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. Assurance with Intelligence. Paul Gerrard. Gerrard. Consulting. 1 Old Forge Close. Maidenhead. Berkshire. SL6 2RD UK. e: paul@gerrardconsulting.com. w: http://gerrardconsulting.com. t: 01628 639173. (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. How does it work? . What is an F-ratio?. What is a grand mean?. What are the degrees of freedom for the F-ratio?. k-1, N-k. Post hoc tests. F-test in ANOVA is the so-called . omnibus test. . It tests the means globally. It says nothing about which particular means are different.. Understand the basic principles of ANOVA. Why it is done?. What it tells us?. Theory of one-way independent ANOVA. Following up an ANOVA. :. Planned contrasts/comparisons. Choosing contrasts. Coding contrasts. 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.. 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.. LM ANOVA 2. 2. Example -- Background. Bacteria -- effect . of temperature (10. o. C & 15. o. C) and relative humidity (20%, 40%, 60%, 80%) on growth rate (cells/d. ).. 120 . petri . dishes with a growth . 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.. Regression Trees. Characteristics of classification models. model. linear. parametric. global. stable. decision tree. no. no. no. no. logistic regression. yes. yes. yes. yes. discriminant. analysis.