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.

Given the provided F-statistics and p-values, let's analyze the results in the context of the significance level \( \alpha = 0.05 \):

1. **For Treatments:**
   - F-statistic = 2.14, p-value = 0.095
   - Since \( p = 0.095 > \alpha = 0.05 \), we **fail to reject** the null hypothesis for treatments. This means there is **no significant difference** in treatment means.

2. **For Blocks:**
   - F-statistic = 3.56, p-value = 0.018
   - Since \( p = 0.018 < \alpha = 0.05 \), 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.**

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Do you want further details or have any questions? 

Here are 5 related questions to expand on this topic:
1. What is the null hypothesis in a two-way ANOVA for treatments and blocks?
2. How do you calculate the F-statistic in a two-way ANOVA?
3. Why is the p-value compared to the significance level \( \alpha \)?
4. What would a significant interaction effect mean in a two-way ANOVA?
5. 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.

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.

Learn how to interpret the F-statistic and p-values in a two-way ANOVA. In this example, with an F-statistic for Treatments of 2.14 and p-value of 0.095, and an F-statistic for Blocks of 3.56 and p-value of 0.018, we conclude there is a significant difference in block means but not in treatment means. Suitable for college-level statistics students.

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