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?