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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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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.

Solution Preview

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

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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