Math Problem Statement
In a two way ANOVA the F statistic for Treatments is 2.14 with p-value of 0.095, and the F statistic for Blocks is 3.56 with p-value of 0.018. What can you conclude from this? Assume α=0.05.
Multiple choice question.
There is a significant difference in block means, but not in the treatment means.
There is a significant difference in block means and in the treatment means.
There is a not significant difference in block means and not a significant difference in the treatment means.
There is a not significant difference in block means, but there is a significant difference in the treatment means.
Solution
Given the provided F-statistics and p-values, let's analyze the results in the context of the significance level :
-
For Treatments:
- F-statistic = 2.14, p-value = 0.095
- Since , we fail to reject the null hypothesis for treatments. This means there is no significant difference in treatment means.
-
For Blocks:
- F-statistic = 3.56, p-value = 0.018
- Since , we reject the null hypothesis for blocks. This means there is a significant difference in block means.
Conclusion:
There is a significant difference in block means, but no significant difference in treatment means.
Thus, the correct answer is:
There is a significant difference in block means, but not in the treatment means.
Do you want further details or have any questions?
Here are 5 related questions to expand on this topic:
- What is the null hypothesis in a two-way ANOVA for treatments and blocks?
- How do you calculate the F-statistic in a two-way ANOVA?
- Why is the p-value compared to the significance level ?
- What would a significant interaction effect mean in a two-way ANOVA?
- How does the assumption of homogeneity of variances affect the results of a two-way ANOVA?
Tip: In ANOVA, always check if the interaction between factors (if present) is significant before interpreting main effects like treatments or blocks.
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Math Problem Analysis
Mathematical Concepts
Statistics
ANOVA (Analysis of Variance)
Hypothesis Testing
Formulas
F-statistic = (variance between groups) / (variance within groups)
p-value comparison with significance level α
Theorems
Null Hypothesis: No significant difference in means
Alternative Hypothesis: Significant difference in means
Suitable Grade Level
College-level statistics or AP Statistics
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