1. What is Sum of Squares Between?

The Sum of Squares Between (SS_between) measures the variation between different groups in an analysis of variance (ANOVA). It quantifies how much the group means differ from the overall grand mean.

2. How Does the Calculator Work?

The calculator uses the SS between formula:

Where:

• \( k \) — Number of groups
• \( n_j \) — Size of group j
• \( \bar{x}_j \) — Mean of group j
• \( \bar{x} \) — Grand mean (mean of all observations)

Explanation: The formula calculates the weighted sum of squared deviations of group means from the grand mean.

3. Importance of SS Between

Details: SS between is a key component in ANOVA, helping determine whether group means are significantly different. A larger SS between relative to SS within suggests group means differ more than expected by chance.

4. Using the Calculator

Tips: Enter the number of groups, then for each group provide the group mean and sample size. All values must be valid (group sizes ≥1, means numeric).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SS between and SS within?
A: SS between measures variation between group means, while SS within measures variation within each group.

Q2: How is SS between used in ANOVA?
A: In ANOVA, F-statistic = (SS between/df between)/(SS within/df within), testing if group means differ significantly.

Q3: What does a high SS between value indicate?
A: High SS between suggests group means are quite different from each other and from the grand mean.

Q4: Can SS between be negative?
A: No, since it's a sum of squared values, SS between is always ≥0.

Q5: How does group size affect SS between?
A: Larger groups contribute more to SS between as their deviations from grand mean are weighted by sample size.