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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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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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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EXERCISE 36 Questions to be graded 1. The researchers found a significant difference between the two groups (control and treatment) for change in mobility of the women with osteoarthritis (OA) over 12 weeks with the results of F(1‚ 22) = 9.619‚p = 0.005. Discuss each aspect of these results. Answer F-value shows significance between the two groups. The null hypothesis should be rejected because the P-Value is 0.005 which would mean that the groups are different. 2. State the null hypothesis
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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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Submit your answers to the 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
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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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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 F-test TukeyKramer test Fisher’s Least Significant Difference test Business Statistics: A Decision-Making Approach‚ 6e © 2005 Prentice-Hall‚ Inc. Chap 11-3 General ANOVA Setting Investigator controls one or more independent variables Called factors (or treatment variables)
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ANALYSIS OF VARIANCE? WHAT NULL HYPOTHESIS ISTESTED BY ANOVA? ANALYSIS OF VARIANCE IS A STATISTICAL METHOD USED TO TEST DIFFERENCES BETWEEN TWO OR MORE MEANS. IT IS USED TO TEST GENERAL RATHER THAN SPECIFIC DIFFERENCES AMONG MEANS. THUS THE NULL HYPOTHESIS IS CALLED AN OMNIBUS NULL HYPOTHESIS IT MEANS THAT AT LEAST ONE POPULATION MEAN IS DIFFERENT FROM AT LEASTONE OTHER MEAN. THE ANOVA DOES NOT REVEAL WHICH PAIR IS SIGNIFICANT‚ THUS A FOLLOW UP TEST IS NECESSARY TO DETERMINEWHICH PAIR
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