PPT-ANOVA

Analysis of Variance Martina Litschmannová m artinalitschmannova vsbcz K210 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. 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?. 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. Unweighted. MEANS ANOVA. Data Set “. Int. ”. Notice that there is an interaction here.. Effect of gender at School 1 is 155-110 = 45.. Effect of gender at School 2 is 135-120 = 15.. Weighted means. 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?. 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. ANOVA. Multiple Comparisons. Pairwise Comparisons and . Familywise. Error. . . fw. is the . alpha familywise. , the conditional probability of making one or more Type I errors in a family of . 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.. 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. 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. 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. ANOVA makes assumptions about error for significance tests. What are the assumptions?. What might happen (why would it be a problem) if the assumption of {normality, equality of error, independence of error} turned out to be false?.