PPT-Contrasts in ANOVA Decomposition of Treatment Sums of Squares using prior information

1 Contrasts notation For a Oneway ANOVA a contrast is a specific comparison of Treatment group means Contrast constants are composed to test a specific hypothesis related to Treatment means based upon some prior information about the Treatment groups For k treatment groups contrast constants are a sequence of numbers . When applied to generalized l inear models multilevel models and other extensions of classical regression ANOVA can be e xtended in two di64256erent directions First the Ftest can be used in an asymptotic or approximat e fashion to compare nested mo 1. Inferior parietal involvement in long term memory. There is a hypothesis that different brain regions are recruited during recall processes. A distinction between recognition -> I remember details of learning how to calculate contrasts, like who taught me and why. and familiarity -> I have a vague notion that contrasts were described to me at some point.. Cal State Northridge. . 320. Andrew Ainsworth PhD. Topics in Factorial Designs. What is Factorial?. Assumptions. Analysis. Multiple Comparisons. Main Effects. Simple Effects. Simple Comparisons. Effect Size estimates. Cal State Northridge. . 320. Andrew Ainsworth PhD. 2. Major Topics. What are repeated-measures?. An example. Assumptions. Advantages and disadvantages. Effect size. Psy 320 - Cal State Northridge. scalability . improvements . and . applications . to . difference . of convex programming.. Georgina . Hall. Princeton, . ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. Nonnegative polynomials. (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 . . In this Lecture we study whether changes . in the independent variables cause changes in the mean . response and we analyze . the data using a method known as analysis . of variance . scalability . improvements . and . applications . to . difference . of convex programming.. Georgina . Hall. Princeton, . ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. Nonnegative polynomials. 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. Type I and Type III Sums of Squares. 1. Confounding in Unbalanced Designs. When designs are “unbalanced”, typically with missing values, our estimates of Treatment Effects can be biased.. When designs are “unbalanced”, the usual computation formulas for Sums of Squares can give misleading results, since some of the variability in the data can be explained by two or more variables.. 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. scalability . improvements . and . applications . to . difference . of convex programming.. Georgina . Hall. Princeton, . ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. Nonnegative polynomials. 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?.