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.