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    ANOVA Effect Size

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    Independent variable: Teaching methods (here we have three teaching methods so we have three levels of independent variable)

    Dependent variable: Mathematics scores

    Null Hypothesis (Ho): There is no significant difference between the population average scores of mathematics among these three groups with different teaching method.

    Alternative Hypothesis (Ho): There is a significant difference between the population average scores of mathematics among these three groups with different teaching method. At least two group have different mean scores.

    Level of significance = 0.05

    Data is given below:

    Student Method 1 Method 2 Method 3
    1 2 1 3
    2 3 2 4
    3 4 5 1
    4 2 6 0
    5 6 2 4
    6 7 5 3

    ANOVA Output is given below:

    Anova: Single Factor

    SUMMARY
    Groups Count Sum Average Variance
    Method 1 6 24 4 4.4
    Method 2 6 21 3.5 4.3
    Method 3 6 15 2.5 2.7

    ANOVA
    Source of Variation SS df MS F P-value F crit
    Between Groups 7 2 3.5 0.921053 0.41948 3.68232
    Within Groups 57 15 3.8

    Total 64 17

    We can see that the P-value of ANOVA table is 0.41948 which is bigger than the 5% level of significance. So we do not have enough evidence to reject our null hypothesis and we can conclude that there is no significant difference between the population average scores of mathematics among these three groups with different teaching method.

    Note: No post hoc test is possible in this case as the null hypothesis is not rejected.

    What is the effect size of the ANOVA?

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    https://brainmass.com/statistics/analysis-of-variance/anova-effect-size-524259

    Solution Preview

    When using effect size with ANOVA, we use Eta squared, which is defined as ...

    Solution Summary

    The teaching methods for ANOVA effect size are determined. The significant differences between the population average scores of mathematics among the three groups with different teaching methods are provided.

    $2.49

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