Chapter 16 Completely Randomized Factorial ANOVA This tutorial describes the procedures for computing F tests for a completely randomized factorial analysis of variance design. The reading-speed data in Table 16.4-2 of the textbook are used to illustrate the procedures. 1. Enter a description of the data in the SPSS Data Editor following steps 1–4 described in the Frequency Distribution tutorial for Chapter 2. Use rows 1‚ 2‚ and 3 of the SPSS Data Editor Variable View window to describe
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A 4(amount of alcohol: 0‚ 2‚ 4‚ 6 pints) X 2(type of lighting: dim‚ bright) within subjects Factorial ANOVA was conducted on attactiveness scores of chosen mate. Mauchly’s test indicated that the assumption of sphericity had been assumed for the main effect of alcohol amount‚ χ²(5) = 4.70‚ p > .05 and alcohol amount and lighting type interaction effect‚ χ²(5) = 2.58‚ p > .05. There was a significant main effect of type of lighting on attractiveness of chosen mate‚ F (1‚ 25) = 23.42‚ p
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Analysis of Variance (ANOVA) Indian Institute of Public Health Delhi MSc CR 2013-15 Outline of the session • Need for Analysis of Variance • Concept behind one way ANOVA • Example • Non-parametric alternative When dependent variable is continuous Type of Dependent variable Type of Independent variable Number of Groups Continuous Categorical More than two Non-parametric (Wilcoxon sign rank) Paired t – test Not normal Non-parametric (Wilcoxon sign
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26 3.04 2.8 3.75 3.64 3.65 3.18 3.44 3.51 2.81 3.64 2.85 3.56 2.92 3.35 3.46 3.59 3.65 2.97 3.21 3.65 2.94 3.53 3.65 3.61 3.7 2.91 3.77 3.79 3.59 3.38 3.57 2.97 3.44 3.48 2.99 3.73 2.91 3.78 3.13 3.14 SUMMARY Groups Unemployed Part-time Full-time ANOVA Source of Variation Treatment Error Total Null hypothesis: Alternate hypothesis: Significance level: p-Value Decision: Count 25 45 130 0 0 Sum 82.110 152.050 450.130 0.000 0.000 Average 3.284 3.379 3.463 Variance 0.110 0.085 0.091 SS 0.771 18
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ADVANTAGES OF THE FACTORIAL DESIGN Some experiments are designed so that two or more treatments (independent variables) are explored simultaneously. Such experimental designs are referred to as factorial designs. In factorial designs‚ every level of each treatment is studied under the conditions of every level of all other treatments. Factorial designs can be arranged such that three‚ four‚ or n treatments or independent variables are studied simultaneously in the same experiment. If two independent
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Variance (ANOVA) Dr. H. Johnson ANOVA • Analysis of variance (ANOVA) is a powerful hypothesis testing procedure that extends the capability of t-tests beyond just two samples. • Many types of ANOVAs‚ today we will learn about a oneway independent-measures ANOVA • Later we’ll learn one-way repeated-measures ANOVA . • We’ll also learn two-factor ANOVA after that. • These ANOVAs are by no means all of them! There are a LOT more types! One-Way ANOVA • The independent measures ANOVA is used
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Chapter 15: Introduction to the Design of Experimental and Observational Studies The Models in Analysis of Variance(ANOVA) and in Regression are different. In regression model‚ all the response and predictors are continuous (quantitative) variables. However‚ in ANOVA model‚ the response is continuous but the predictors are categorical (qualitative) variables. There are some concepts here. 1. Factor and factor level. A factor is a predictor (explanatory or independent) variable. A factor level is
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Iqra University‚ Main Campus Course: Statistical Inferences Faculty: Iftikhar Mubbashir Date: December 5‚ 2013 Fall 2013 Statistics-Walpole Chapter-12 One way Classification • • • • • • Random samples of size n are selected from each of k populations. The k populations are independent and normally distributed with means µ 1 ‚ µ 2 ‚K ‚ µ k and common variance σ 2 . We wish to derive appropriate methods for testing the hypothesis:
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procedures Set up and perform randomized blocks analysis Analyze two-factor analysis of variance test with replications results Business Statistics: A Decision-Making Approach‚ 6e © 2005 Prentice-Hall‚ Inc. Business Statistics: A Decision-Making Approach‚ 6e Chap 11-2 © 2005 Prentice-Hall‚ Inc. Chapter 11 11-2 Student Lecture Notes Chapter Overview Analysis of Variance (ANOVA) One-Way ANOVA Randomized Complete Block ANOVA Two-factor ANOVA with replication F-test
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distribution of all possible values of the f statistic is called an F distribution‚ with v1 = n1 - 1 and v2 = n2 - 1 degrees of freedom Analysis of variances (ANOVA) One way ANOVA: A One-Way Analysis of Variance is a way to test the equality of three or more means at one time by using variances. Two way ANOVA: A Two-Way ANOVA is useful when we desire to compare the effect of multiple levels of two factors and we have multiple observations at each level. Grand Mean The grand mean of
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