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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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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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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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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How to Use a Data Spreadsheet: Excel One does not necessarily have special statistical software to perform statistical analyses. Microsoft Office Excel can be used to run statistical procedures. Although in some respects Excel is not as preferable for data analyses as IBM SPSS‚ it is very userfriendly with simpler statistical procedures. This appendix describes how to use Excel to execute basic statistical calculations. Data from the 2004 version of the General Social Survey (GSS) is used for
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Getting Started in Excel Many of the editing tools that you use in Excel are similar to Word and PowerPoint You will need to become familiar with a few new things for Excel: Rows‚ Columns‚ Various Formulas‚ and Charts just to name a few When you see a reference such as A7‚ A is the column and 7 is the row‚ this will give you the particular cell that is being referenced. You will learn that you can click or enter in information when it comes to cells and formulas. Everyone will have their own
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didn’t know what a spreadsheet was‚ etc. So I started at: http://en.wikipedia.org/wiki/Spreadsheet. I read that and got a good base of spreadsheets and the history. First of all‚ Microsoft Excel is the industry standard in spreadsheets (history on spreadsheets can be accessed at the above website address). With Excel‚ you can create a shared workbook and place it on a network location where several people can edit‚ change‚ and work on the contents of a workbook‚ I discovered. Therefore‚ if the people
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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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