Estimate a variance ratio

Estimate relative spread in two independent, approximately normal samples.

Guides · Basic statistics · 4 min read

Example: Cell A versus Cell B strength variation

45 independent pouch-strength readings per packaging cell. Sample 1 is Cell A and Sample 2 Cell B.

Download the study reference (CSV)

This is the same example used in Help. The CSV is a reference for the supplied study. Enter the checked summaries manually on Inputs; importing the CSV does not populate this calculator. Use Open example in a practice copy in Help to prefill the inputs.

1. Create the workspace

In the sidebar, open Basic Statistics and choose Confidence Intervals. Create an analysis, name it, select New blank worksheet, then choose Create analysis.

2. Choose the interval

On Inputs, choose Variance ratio (F) for Parameter. Enter 0.95 in Confidence level (0–1) for a 95% interval.

3. Enter the summaries

Under Summarized data, enter the following values. Keep the full precision shown for standard deviations. No worksheet columns are assigned.

Enter 45 in Sample size (n₁).

Enter 45 in Sample size (n₂).

Enter 1.053112894079627 in Sample standard deviation (s₁).

Enter 1.543914152111739 in Sample standard deviation (s₂).

Sample 1 is Cell A; Sample 2 is Cell B.

Confidence Intervals: Inputs with the example’s assignments and settings
Inputs with the selected population parameter, 95% confidence level and entered sample summaries. View full-size image (opens in a new tab)

4. Run analysis

Choose Run analysis, then open Results.

5. Interpret results

  1. Identify what the interval estimates

    45 independent pouch-strength readings per packaging cell. Sample 1 is Cell A and Sample 2 Cell B. The selected parameter is Variance ratio (F).

  2. Read the estimate and bounds

    Cell A variance divided by Cell B variance is 0.4653, with a 95% interval of 0.2557–0.8467. The ratio has no unit.

  3. Keep the interpretation clear

    The entire interval is below 1, supporting lower variation in Cell A under normal-population and independence assumptions. This is a ratio of variances, not standard deviations.

  4. Use the uncertainty in the decision

    Check material, sampling and measurement conditions before attributing the difference to the packaging cell. The result compares spread, not mean strength.

More details: read each result section

Complete result tables use six significant digits, as in Help.

Confidence interval

Parameter names the population quantity. Confidence level 0.95 means this interval method covers the fixed population parameter in 95% of repeated comparable samples under its assumptions. Estimate is the sample-based value; Lower bound and Upper bound mark its uncertainty. Method records the calculation. The entire interval is below 1, supporting lower variation in Cell A under normal-population and independence assumptions. This is a ratio of variances, not standard deviations.

Confidence interval · 6 rows
StatisticValue
ParameterVariance ratio (F)
Confidence level0.95
Estimate0.465268
Lower bound0.255683
Upper bound0.846652
MethodF-based

6. Create a report

Keep the complete Confidence interval table, selected parameter, confidence level, method and entered summaries. The entire interval is below 1, supporting lower variation in Cell A under normal-population and independence assumptions. This is a ratio of variances, not standard deviations.

Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.

Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.

Complete native output for this Help example, including applicable tables, charts and run notes. Report numbers use the app’s displayed precision. Exported charts are static. On narrow screens, scroll wide charts and tables sideways.
View example report: Compare seal-strength variances

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