Chi Squared Test Sample Size Calculator

Calculator Inputs

Study label

Test type

Significance level alpha

Desired power

Effect size preset

Custom effect size w

Rows for table test

Columns for table test

Goodness of fit categories

Estimated parameters

Manual degrees of freedom

Dropout or unusable data percent

Design effect

Example Data Table

Scenario	Test Type	Alpha	Power	Effect Size w	Degrees of Freedom	Planning Note
Brand preference survey	Goodness of fit	0.05	0.80	0.30	3	Four categories with medium effect.
Treatment response table	Independence	0.05	0.90	0.20	2	Smaller effect needs more observations.
Regional outcome comparison	Homogeneity	0.01	0.80	0.25	6	Strict alpha raises sample needs.

Formula Used

The calculator uses Cohen's chi squared effect size and a noncentral chi squared power model.

Noncentrality: λ = N × w²

Critical value: χ²crit = inverse central χ² CDF at 1 − α with df.

Power: Power = P[χ²(df, λ) > χ²crit]

Search rule: increase N until calculated power reaches the target power.

Goodness of fit df: df = categories − 1 − estimated parameters.

Table df: df = (rows − 1) × (columns − 1).

Adjusted enrollment: enrolled N = analyzable N × design effect ÷ (1 − dropout rate).

How to Use This Calculator

Select the chi squared test design first. Enter alpha and target power. Choose an effect size preset or enter your own Cohen's w. Add rows and columns for a table test. Add category count for a goodness of fit test. Use manual degrees of freedom for custom designs. Enter dropout and design effect when planning enrollment. Press calculate. Download the CSV or PDF when you need a saved report.

Understanding Chi Squared Test Sample Size

A chi squared test needs enough observations to detect a real pattern. Low sample size can hide useful differences. It can also create weak expected counts. This calculator estimates the minimum analyzable sample size for a target power level. It supports goodness of fit, independence, homogeneity, and manual degrees of freedom.

Why Power Matters

Power is the chance of rejecting a false null hypothesis. A common target is 80 percent. Higher power gives stronger protection against missed effects. It also increases the required sample size. The alpha level controls the chance of a false positive. Many studies use 0.05, but stricter studies may use 0.01.

Effect Size Choice

The calculation uses Cohen's w. A value near 0.10 is small. A value near 0.30 is medium. A value near 0.50 is large. Smaller effects need larger samples because the difference is harder to see. Use a pilot study, prior research, or practical judgement when choosing w.

Degrees of Freedom

Degrees of freedom depend on the test design. For goodness of fit, use categories minus one. Subtract estimated parameters when needed. For an independence table, use rows minus one times columns minus one. More degrees of freedom usually change the critical value and required sample size.

Practical Planning Notes

The first result is the analyzable sample size. That is the number needed after missing data. The adjusted enrollment size includes dropout and design effect. Design effect is useful when clustering, weighting, or complex sampling reduces information. A value of 1 means simple random sampling.

Expected Counts

Chi squared tests work best when expected cell counts are not too small. Many simple teaching rules target at least five expected observations per cell. This calculator reports the average expected count. Review sparse tables carefully. Exact, simulated, or merged category methods may be better for very small counts.

Using The Result

Treat the output as a planning guide. Confirm assumptions before data collection starts. Save the CSV for spreadsheets. Use the PDF for notes or reports. If your design is unusual, compare results with statistical software before final approval. Document every chosen assumption. This makes review easier and improves repeated study planning later workflows.

FAQs

What is Cohen's w?

Cohen's w is a chi squared effect size. It measures how far observed proportions are expected to move from null proportions. Larger values need fewer observations.

Can I enter power as 80?

Yes. The calculator converts values above 1 into percentages. So 80 becomes 0.80. You may also enter 0.80 directly.

Which test type should I choose?

Use goodness of fit for one categorical variable. Use independence or homogeneity for contingency tables. Use manual degrees of freedom for special designs.

Why is adjusted enrollment larger?

Adjusted enrollment includes expected dropout and design effect. It estimates how many people or records you should recruit before data loss happens.

What alpha should I use?

Many studies use 0.05. Use 0.01 for stricter evidence. Smaller alpha values usually require larger sample sizes.

Does this check every cell count?

It reports average expected count only. Real tables may have uneven expected values. Check expected counts again after planning your table structure.

Can this replace statistical software?

It is useful for planning and fast estimates. For regulated studies, confirm assumptions and final power with specialist statistical software.

What happens with a tiny effect size?

A tiny effect size may require a very large sample. If no result appears, review whether the effect size is realistic for your study.