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ANOVA Between-Subject Design: A conceptual approach

ANOVA Between-Subject Design: A conceptual approach. Chong Ho (Alex) Yu. Objective. Illustrate the purpose, the concept, and the application of ANOVA between-subject design

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ANOVA Between-Subject Design: A conceptual approach

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  1. ANOVA Between-Subject Design: A conceptual approach Chong Ho (Alex) Yu

  2. Objective • Illustrate the purpose, the concept, and the application of ANOVA between-subject design • will NOT walk through the procedure of hand-calculation; you will use a statistical software package to do your exercises. • By the end of the lesson you will understand the meaning of the following concepts: • One-way ANOVA vs. Two-way ANOVA • Grouping factor and level • Between-subject and within-subject • Parametric assumptions • Variance and F-ratio • Confidence intervals and diamond plots

  3. What is ANOVA? • Analysis of variance: a statistical procedure to compare the mean difference • Null hypothesis: all means are not significantly different from each other • Alternate: Some means are not equal

  4. One-way ANOVA There must be three or more groups. If there are two groups only, you can use a 2-independent-sample t-test. The independent variable is called the grouping factor. The group is called the level. In this example, there is one factor and three levels (Group 1-3). .

  5. Two-way ANOVA • There are two grouping factors. • Unlike one-way ANOVA, in this design it is allowed to have fewer than three levels (groups) in each factor. • In this example, there are two factors: A and B. In each factor, there are two levels: 1 and 2. Thus, it is called a 2X2 ANOVA between-subject design. • In this lesson we focus on one-way ANOVA only, but you need to know why on some occasions there are only two groups in ANOVA.

  6. What is between-subject? Between-subject: The subjects in each level (group) are not the same people (independent).

  7. What is within-subject? Within-subject: The subjects in each level are the same people (correlated). They are measured at different points of time. In this lesson we will focus on the between-subject ANOVA only

  8. Why isn’t it called Analysis of means? If we want to compare the means, why is it called Analysis of Variance, not Analysis of Mean?

  9. Why isn’t it called Analysis of means? • In the unreal world, the people in the same group have the same response to the treatment: • All people in Group 1 got 10. • All people in Group 2 got 11. • All people in Group 3 got 12. • But in the real world, usually there is variability in each group (dispersion). We must take the variance into account while comparing the means.

  10. Parametric assumptions Independence: The responses to the treatment by the subjects in different groups are independent from each other. Normality: The sample data have a normal distribution. the variances of data in different groups are not significantly different from each other.

  11. A hypothetical example Three different teaching formats (levels) are used in three different classes

  12. When we look at the means alone

  13. F ratio • F = signal /noise(error) • Between-group variance is the signal; we want to see whether there is a significant difference (variability) between the groups. • Within-group variance is the noise or the error; it hinders us from seeing the between-group difference when the within-group variances overlap. • F = mean square between / mean square within • MSB = Sum of square between / DF between • MSW = Sum of square within/ DF within • Effect size = eta square = SS effect (between) / SS total

  14. ANOVA results • Mean square between and mean square error  F ratio  Probability (p value) • The p value is smaller than .05 and therefore we reject the null hypothesis. • Somewhere there is a difference. • But, where is the difference? Which group can significantly outperform which? • Many textbooks go into multiple comparison procedures or post hoc contrast at this point, but let’s try something else.

  15. Diamond plots • Grand sample mean: represented by a horizontal dot line  • Group means: the horizontal line inside each diamond is the group means  • Confidence intervals: The diamond is the CI for each group

  16. Assignment 15 Download the dataset one_way.jmp from the Ch15 folder. Run a one-way ANOVA with this hypothesis: There is no significant difference between difference academic levels in test performance. Use level as the IV and score as the DV Use Test of unequal variances to check whether the group variances are equal. If OK, create a diamond plot. Is there any performance gap?

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