Calculator
Paste student scores for two groups. The calculator compares score variance and reports the F statistic, p value, and decision.
Example Data Table
| Student | Section A | Section B |
|---|---|---|
| 1 | 78 | 71 |
| 2 | 81 | 75 |
| 3 | 85 | 80 |
| 4 | 88 | 83 |
| 5 | 90 | 77 |
| 6 | 84 | 74 |
| 7 | 79 | 82 |
| 8 | 87 | 86 |
Formula Used
Sample variance for each group:
s² = Σ(xᵢ - x̄)² / (n - 1)
F statistic:
F = larger sample variance / smaller sample variance
Degrees of freedom:
df1 = n₁ - 1 and df2 = n₂ - 1
Decision rule: compare the calculated F statistic with the critical F value at your chosen significance level. This page also estimates the two tailed p value from the F distribution.
How to Use This Calculator
- Enter a name for each score group.
- Paste the scores for both groups using commas, spaces, or new lines.
- Choose the significance level, such as 0.05.
- Set the number of decimal places you want.
- Click Calculate F Test to show the result above the form.
- Review the graph, decision, and detailed table.
- Download the result as CSV or PDF when needed.
FAQs
1. What does the F test score calculator measure?
It compares the variance of two score groups. This helps you see whether one class, section, or assessment set shows significantly more score spread than the other.
2. Why does the calculator place the larger variance in the numerator?
Doing that keeps the F statistic at or above 1. It also makes the result easier to interpret when checking whether score variability differs across groups.
3. What kind of scores can I enter?
You can enter quiz scores, exam scores, assignment marks, rubric totals, or any numeric student performance values. Separate numbers with commas, spaces, or line breaks.
4. What does the p value tell me?
The p value estimates how likely your variance difference would appear if the group variances were actually equal. Smaller p values suggest stronger evidence of unequal variance.
5. What significance level should I use?
A common choice is 0.05. If you want stricter evidence before calling the variances different, choose a smaller value like 0.01.
6. Can I use this before running a t test?
Yes. Many teachers and analysts check variance equality first, especially when comparing two groups and deciding which follow-up statistical method fits best.
7. Why do both groups need at least two scores?
Variance uses sample spread around the mean. With fewer than two values, variance cannot be estimated correctly for an F test.
8. What should I do if both groups have zero variance?
That means every score inside a group is identical. An F test is not useful there because the variance ratio becomes undefined or uninformative.