Let's analyze and fill in the missing values in this ANOVA summary table.

Given Information

• Sum of Squares (S.S.):

  • Between: 1475.88
  • Within: 1624.00
  • Total: 3099.88

• Degrees of Freedom (d.f.):

  • Between: 7
  • Within: 58
  • Total: 65

• Mean Square (M.S.):

  • Between: 210.84
  • Within: Missing (denoted by the key symbol)

Calculations

1. Mean Square (M.S.) for "Within"

The Mean Square for each category is calculated as: $\text{M.S.} = \frac{\text{S.S.}}{\text{d.f.}}$

So, for the Within category: $\text{M.S. (Within)} = \frac{1624.00}{58} = 28.00$

2. F-Ratio (F)

The F-ratio is calculated as: $F = \frac{\text{M.S. (Between)}}{\text{M.S. (Within)}}$

Substituting the values: $F = \frac{210.84}{28.00} = 7.53$

Completed ANOVA Table

The missing values are:

• M.S. (Within) = 28.00
• F = 7.53

So the completed table is:

Would you like further details or explanations on any part of this process?

Related Questions

1. How is the F-ratio used to determine statistical significance?
2. What do Sum of Squares values indicate in an ANOVA?
3. How can degrees of freedom affect the Mean Square value?
4. Why is the Total S.S. the sum of Between and Within S.S.?
5. What are typical threshold values for the F-ratio in hypothesis testing?

Tip

In ANOVA, higher F-values typically indicate a greater likelihood that the group means differ significantly.