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Introduction to ANOVA
- 1. Introduction to ANOVA Presented by ;- Akash Ghanate 2018BBA01 Subject :- BUSINESS RESEARCH
- 2. Contents to be covered Definition * Types of ANOVA * WHY DO AN ANOVA, NOT MULTIPLE T-TESTS? * Why ANOVA instead of multiple t-tests? * ANOVA Assumptions * ANOVA examples *
- 3. Analysis of Variance Definition Analysis of variance (ANOVA) is a statistical test for detecting differences in group means when there is one parametric dependent variable & one or more independent variables.
- 4. Extra about ANOVA Many studies involve comparisons between more than two groups of subjects. If the outcome is numerical, ANOVA can be used to compare the means between groups. ANOVA is an abbreviation for the full name of the method: ANalysis Of Variance If the outcome is numerical, ANOVA can be used to – Invented by R.A. Fisher in the 1920’s
- 5. Why do an ANOVA? when there are 3 or more means being compared, statistical significance can be ascertained by conducting one statistical test, ANOVA, or by repeated t-tests. Why not conduct repeated t-tests? Each statistical test is conducted with a specified chance of making a type I–error—the alpha level.
- 7. ONE-WAY ANOVA A one-way ANOVA has just one independent variable. For example, difference in IQ can be assessed by Country, and County can have 2, 20, or more different categories to compare.
- 8. TWO-WAY ANOVA A two-way ANOVA (are also called factorial ANOVA) refers to an ANOVA using two independent variables. Expanding the example above, a 2-way ANOVA can examine differences in IQ scores (the dependent variable) by Country (independent variable 1) and Gender (independent variable 2).
- 9. N-Way ANOVA A researcher can also use more than two independent variables, and this is an n-way ANOVA (with n being the number of independent variables you have). For example, potential differences in IQ scores can be examined by Country, Gender, Age group, Ethnicity, etc, simultaneously.
- 10. How do types of ANOVA differs ANOVA ONE-WAY ANOVA TWO-WAY ANOVA One independent variable Only one ‘p’ value is obtained Two independent Variables Three different ‘p’ values are obtained Outcome of factorial Design
- 11. Why ANOVA instead of multiple t-tests? If you are comparing means between more than two groups, why not just do several two sample t-tests to compare the mean from one group with the mean from each of the other groups? Before ANOVA, this was the only option available to compare means between more than two groups. The problem with the multiple t-tests approach is that as the number of groups increases, the number of two sample t-tests also increases. As the number of tests increases the probability of making a Type I error also increases.
- 12. If variability between groups is large relative to the variability within groups, the F-statistic will be large. If variability between groups is similar or smaller than variability within groups, the F-statistic will be small. If the F-statistic is large enough, the null hypothesis that all means are equal is rejected. ANOVA: F-statistic
- 13. ANOVA assumptions The observations are from a random sample and they are independent from each other The observations are normally distributed within each group The variances are approximately equal between groups It is not required to have equal sample sizes in all groups.
- 14. THE NULL HYPOTHESIS AND ALPHA LEVEL The null hypothesis is that all the groups have equal means. The alternative hypothesis is that there is at least one significant difference between the means Level of significance α is selected as 0.05 The test statistic for ANOVA is the ANOVA F-statistic. Ho µ 1= µ 2= µ 3 = µk
- 15. A scientist wants to know if all children from schools A, B and C have equal mean IQ scores. Each school has 1,000 children. It takes too much time and money to test all 3,000 children. So a simple random sample of n = 10 children from each school is tested. SIMPLE EXAMPLE
- 16. Right, so our data contain 3 samples of 10 children each with their IQ scores. Running a simple descriptives table immediately tells us the mean IQ scores for these samples. The result is shown below. DESCRIPTIVES TABLE
- 17. For making things clearer, let's visualize the mean IQ scores per school in a simple bar chart. Clearly, our sample from school B has the highest mean IQ - roughly 113 points. The lowest mean IQ -some 93 points- is seen for school C.Now, here's the problem: our mean IQ scores are only based on tiny samples of 10 children per school. So couldn't it be that
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