1. What is Sum of Squares Within?

The Sum of Squares Within (SS_within) measures the variation within individual groups in ANOVA (Analysis of Variance). It quantifies how much the data points within each group deviate from their respective group means.

2. How Does the Calculator Work?

The calculator uses the SS_within formula:

Where:

• \( k \) — Number of groups
• \( n_j \) — Number of observations in group j
• \( x_{ij} \) — The ith observation in group j
• \( \bar{x}_j \) — Mean of group j

Explanation: The formula calculates the squared deviations of each observation from its group mean and sums them across all groups.

3. Importance of SS_within in ANOVA

Details: SS_within is a key component in ANOVA, used to calculate the within-group variance. It helps determine whether observed differences between group means are statistically significant.

4. Using the Calculator

Tips: Enter the number of groups first, then provide comma-separated values for each group. The calculator will compute the sum of squared deviations within each group.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SS_within and SS_between?
A: SS_within measures variation within groups, while SS_between measures variation between group means.

Q2: How is SS_within used in the F-test?
A: The F-statistic in ANOVA is calculated as (SS_between/df_between)/(SS_within/df_within).

Q3: What does a large SS_within indicate?
A: Large SS_within suggests considerable variation within groups, making it harder to detect differences between groups.

Q4: Can SS_within be zero?
A: Only if all values within each group are identical (no variation within groups).

Q5: How does sample size affect SS_within?
A: SS_within typically increases with more observations, but the mean square (SS/df) is what matters for ANOVA.