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make this flow: In addition to the ANOVA, the Tukey test compares means between all possible pairs of groups. In this case, there were six
make this flow: In addition to the ANOVA, the Tukey test compares means between all possible pairs of groups. In this case, there were six comparisons: third vs. fourth, third vs. fifth, third vs. sixth, fourth vs. fifth, fourth vs. sixth, and fifth vs. sixth grades. The results of the Tukey HSD test showed the mean difference between the third and fourth grades was not statistically significant (q-stat = 1.08, p-value = 0.857). Similarly, the mean difference between the fourth and fifth grades (q-stat = 2.85, p-value = 0.196) and between the fourth and sixth grades (q-stat = 3.59, p-value = 0.067) were also not statistically significant. The mean difference between the fifth and sixth grades was also not statistically significant (q-stat = 0.79, p-value = 0.899). However, the mean differences between the third and fifth grades (q-stat = 4.35, p-value = 0.017), and between the third and sixth grades (q-stat = 5.22, p-value = 0.003) were statistically significant. These results suggest that while there are no significant differences in means between the fourth, fifth, and sixth grades, there are significant differences between the third grade and both the fifth and sixth grades
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