The following data represent the results from an independent-measures study comparing two treatment conditions.

Treatment
One	Treatment
Two
4.5	5.7
3.5	4
4.2	5.1
4.8	4.4
4.2	2.6
4.3	3

Conduct ANOVA with
for this data and calculate the
-ratio and
-value. Round your answer to three decimal places. Assume all population and ANOVA requirements are met.

F-ratio:
0.051
Correct

To conduct an ANOVA and calculate the F-ratio for the given data from an independent-measures study comparing two treatment conditions, we need to follow these steps:

### Data
- **Treatment One:** 4.5, 3.5, 4.2, 4.8, 4.2, 4.3
- **Treatment Two:** 5.7, 4, 5.1, 4.4, 2.6, 3

### Step 1: Calculate the Means
Calculate the mean of each treatment group.

\[
\text{Mean of Treatment One} (\bar{X_1}) = \frac{4.5 + 3.5 + 4.2 + 4.8 + 4.2 + 4.3}{6}
\]
\[
\text{Mean of Treatment Two} (\bar{X_2}) = \frac{5.7 + 4 + 5.1 + 4.4 + 2.6 + 3}{6}
\]

### Step 2: Calculate the Variance within Treatments (SSW)
Calculate the sum of squares within each treatment group.

\[
SSW_1 = \sum (X_i - \bar{X_1})^2
\]
\[
SSW_2 = \sum (X_i - \bar{X_2})^2
\]
\[
SSW = SSW_1 + SSW_2
\]

### Step 3: Calculate the Variance between Treatments (SSB)
Calculate the sum of squares between treatments.

\[
SSB = n_1(\bar{X_1} - \bar{X_G})^2 + n_2(\bar{X_2} - \bar{X_G})^2
\]
where \(\bar{X_G}\) is the grand mean.

### Step 4: Calculate the Mean Squares (MS)
\[
\text{MSB} = \frac{SSB}{k-1}
\]
\[
\text{MSW} = \frac{SSW}{N-k}
\]

### Step 5: Calculate the F-ratio
\[
F = \frac{\text{MSB}}{\text{MSW}}
\]

### Step 6: Calculate the p-value
The p-value is determined by the F-distribution with degrees of freedom \(df_1 = k-1\) and \(df_2 = N-k\).

Let's perform these calculations now.The calculated F-ratio for the given data is approximately **0.051**, and the p-value is approximately **0.826**.

These results suggest that there is no statistically significant difference between the two treatment conditions, given the high p-value (which is well above the common significance level of 0.05).

If you need further details or have any questions, feel free to ask!

Here are 5 related questions you might consider:
1. What is the interpretation of a high p-value in the context of ANOVA?
2. How does the F-ratio relate to the variation within and between groups?
3. What assumptions must be met to perform a valid ANOVA?
4. How would you interpret the results if the p-value were below 0.05?
5. What are post-hoc tests, and when are they used after ANOVA?

**Tip:** Always check the assumptions of normality and homogeneity of variances before conducting an ANOVA to ensure the validity of your results.

Learn how to conduct ANOVA and calculate the F-ratio and P-value for an independent measures study comparing two treatment conditions. Detailed step-by-step solution with data analysis. Suitable for advanced undergraduate students and researchers.

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