Question

Arrange the steps involved in the calculations of the analysis of variance (ANOVA) for independent groups. - Calculate the grand sum of x^2 by adding the sums of the squared scores of each group. - Calculate a grand sum of X by adding the sums of each group of scores. - Calculate the total sum of squared (SSt), the sum of squares between groups (SSb) and the sum of the squares within groups (SSw) - Calculate the F-ratio and refer to the F distribution of the F-ratio is significant. - Calculate the mean square for the sum of squared between groups (MSb) and the mean square for the sum of squares within groups (MSw). - Calculate the correction factor ( C)

Answer 1

In the analysis of variance (ANOVA) for independent groups, the correct sequence of steps includes calculating the correction factor (C), grand sums, sum of squares (total, between groups, within groups), mean squares, the F-ratio, and finally determining the significance by referencing the F distribution.

Step-by-step explanation:

Steps for Calculating ANOVA for Independent Groups

To perform analysis of variance (ANOVA) correctly for independent groups, there is a specific sequence of calculations that must be conducted. Below are the steps arranged in order:

1. 
   
3. Calculate the correction factor (C), which is used to adjust the sums of squares for any differences in sample sizes.
4. 
   
6. Calculate a grand sum of X by adding the sums of each group of scores. This is the total sum of all the scores across all groups.
7. 
   
9. Calculate the grand sum of x2 by adding the sums of the squared scores of each group. This step is essential for obtaining the total variability in the data.
10. 
    
12. Calculate the total sum of squares (SSt), the sum of squares between groups (SSb), and the sum of squares within groups (SSw). This is where we find out how much of the total variation is due to differences between groups (SSb) and how much is due to differences within groups (SSw).
13. 
    
15. Calculate the mean square for the sum of squared between groups (MSb) and the mean square for the sum of squares within groups (MSw). The mean squares are calculated by dividing each sum of squares by its respective degrees of freedom.
16. 
    
18. Calculate the F-ratio by dividing the mean square between groups (MSb) by the mean square within groups (MSw). The F-ratio is the test statistic used to determine if the mean differences between groups are statistically significant.
19. 
    
21. Refer to the F distribution to determine if the F-ratio is significant. This involves comparing the calculated F-ratio to a critical value from the F distribution table, taking into account the degrees of freedom for both the numerator and the denominator.

The F-ratio is critical in one-way ANOVA and is influenced by differences among group means. A significant F-ratio suggests that there are statistically significant differences between the group means.