To find MS Between (Mean Square Between groups), you calculate it by dividing the Sum of Squares Between groups (SSB) by the between-group degrees of freedom.
Understanding MS Between
MS Between is a key component of ANOVA (Analysis of Variance). It represents the variance between the different groups being compared in the study. A higher MS Between indicates greater variability between the group means compared to the variability within each group.
Formula for MS Between
The formula to calculate MS Between is:
MSB = SSB / dfB
Where:
- MSB = Mean Square Between groups
- SSB = Sum of Squares Between groups
- dfB = Degrees of Freedom Between groups
Steps to Calculate MS Between
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Calculate SSB (Sum of Squares Between groups): This measures the variability between the group means and the overall mean. The formula for SSB is:
SSB = Σ ni (x̄i - x̄)2
Where:
- ni = Sample size of group i
- x̄i = Mean of group i
- x̄ = Grand mean (mean of all observations)
- Σ = Summation across all groups
-
Calculate dfB (Degrees of Freedom Between groups): This is the number of groups minus 1.
dfB = k - 1
Where:
- k = Number of groups
-
Calculate MSB (Mean Square Between groups): Divide SSB by dfB.
MSB = SSB / dfB
Example
Let's say you're comparing the test scores of three different teaching methods (Group A, Group B, and Group C).
| Group | Sample Size (n) | Mean (x̄) |
|---|---|---|
| A | 10 | 80 |
| B | 10 | 85 |
| C | 10 | 90 |
The grand mean (x̄) = (80+85+90)/3 = 85
-
Calculate SSB:
SSB = 10(80-85)2 + 10(85-85)2 + 10(90-85)2
SSB = 10(25) + 10(0) + 10(25)
SSB = 250 + 0 + 250
SSB = 500 -
Calculate dfB:
dfB = 3 - 1 = 2
-
Calculate MSB:
MSB = 500 / 2 = 250
Therefore, the MS Between for this example is 250. This value would then be used in the ANOVA F-test to determine if there's a statistically significant difference between the group means.
