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 18.158 df 2 197 MS 0.385 0.092 F 4.180 18.928 199 Upper Conf. Limit 0.244 0.309 0.187 Difference in [4] Treatment Means??? -
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integer number of plants: 0‚ 1‚ 2‚.... Building Q plants costs each firm 3.5 × Q dollars. Each plant produces one unit of SOMA. If firm 1 builds Q1 plants and firm 2 builds Q2 plants‚ the market price p for one unit of SOMA will be 9 − (Q1 + Q2). For example‚ if firm 1 builds 2 plants and firm 2 builds 4 plants‚ the market price will be 9 − (2 + 4) = 3 per unit. At this price firm 1 will make a profit of 2 × 3 − 2 × 3.5 = −1 while firm 2 will make a profit of 4×3−4×3.5 = −2. Assume‚ no firm will build
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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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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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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 a particular form of the factor. Mostly‚ the level can not be compared. 2. Single-factor and multi-factor
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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: H 0 : µ1 = µ 2 = K = µ k Against‚ H 0 : at least two are unequal . Let x ij := The j th observation from the i th population. • Ti := The total of all observations in the sample from the
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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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following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female)‚ marital status has three groups (married‚ single never married‚ divorced)‚ and the means refer to happiness scores (n = 100): What is/are the independent variable(s)? What is/are the dependent variable(s)? What would be an appropriate null hypothesis? Alternate hypothesis? What are the degrees of freedom for 1) gender‚ 2) marital status‚ 3) interaction
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THE LOGIC OF ANOVA ANalysis Of VAriance (commonly abbreviated as ANOVA)‚ more specifically‚ we will take up an application known as one-way ANOVA. Many statisticians think of ANOVA as an extension of the difference of means test because it’s based‚ in part‚ on a comparison of sample means. At the same time‚ however‚ the procedure involves a comparison of different estimates of population variance—hence the name analysis of variance. Because ANOVA is appropriate for research involving three or
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Applying ANOVA and Non Parametric Tests a. What are three lessons you learned relative ANOVA and Nonparametric tests? While doing the simulation; the three lessons learned are as follows: Monitor – the situation Measure – provide measurements‚ accumulate data Improve – provide solutions for improvement. b. As a result of using this simulation‚ what concepts and analytic tools will you be able to use in your workplace (i.e.‚ how do you expect to apply what you learned)? As a result of using
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