14. ANOVA
Introduction to ANOVA
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A school administrator wants to examine whether students' academic performance differs based on the type of instructional method used in their classes. A random sample of students is selected and divided evenly among the three teaching methods. After a semester, all students take the same standardized final exam. An ANOVA test is performed and results in a P-value of . Interpret these results.
A
The P-value is very high, so there is insufficient evidence to suggest that the type of instructional method has an effect on academic performance.
B
At least one method has a different average test score. Reject the null hypothesis.
C
There is no difference in academic performance, but further testing is required to make a definitive conclusion.
D
The P-value is close to 1, suggesting that the type of instructional method has no impact on students' academic performance.
Verified step by step guidance1
Step 1: Understand the problem. The school administrator wants to determine if the type of instructional method (Traditional, Flipped, Online) affects students' academic performance. An ANOVA test is used to compare the means of test scores across the three groups.
Step 2: Recall the null hypothesis for an ANOVA test. The null hypothesis states that there is no difference in the average test scores among the three instructional methods. The alternative hypothesis states that at least one method has a different average test score.
Step 3: Examine the P-value provided. The P-value is 1.403∙10−7, which is extremely small. In hypothesis testing, a small P-value (typically less than 0.05) indicates strong evidence against the null hypothesis.
Step 4: Interpret the results. Since the P-value is much smaller than the typical significance level (e.g., 0.05), we reject the null hypothesis. This suggests that at least one instructional method has a different average test score compared to the others.
Step 5: Analyze the data provided in the table. The test scores for the Flipped method appear consistently higher than those for the Traditional and Online methods. This supports the conclusion that the type of instructional method impacts academic performance, with the Flipped method potentially being more effective.
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