Calculator inputs
Formula used
For two independent means, the calculator uses n1 = (Zα + Zβ)^2 × (1 + 1/r) / d^2 and n2 = r × n1. Here, r is the allocation ratio. For one sample or paired outcomes, it uses n = (Zα + Zβ)^2 / dz^2.
For two proportions, it converts proportions to Cohen h with h = 2asin(√p2) - 2asin(√p1). Then it applies the two group effect size form. For one way group comparison, it uses a planning approximation with N ≈ (Zα + Zβ)^2 × groups / f^2.
The final adjusted count is ceil(base count × design effect / (1 - attrition rate)). All animal counts are rounded upward.
How to use this calculator
- Select the study design that matches the primary endpoint.
- Choose raw values or standardized effect size entry.
- Enter alpha, desired power, allocation, and group count.
- Add standard deviation, proportions, Cohen d, h, or f.
- Enter attrition and design effect for practical planning.
- Press calculate to show results above the form.
- Download CSV or PDF for protocol notes.
Example data table
| Scenario | Design | Effect | Power | Attrition | Use case |
|---|---|---|---|---|---|
| A | Two means | d = 0.50 | 0.80 | 10% | Compare treatment and control means. |
| B | Paired | dz = 0.60 | 0.90 | 5% | Measure each animal before and after exposure. |
| C | Two proportions | p1 = 0.30, p2 = 0.55 | 0.80 | 15% | Compare response rates between groups. |
| D | One way groups | f = 0.25 | 0.80 | 10% | Plan three or more animal groups. |
Why Animal Sample Size Matters
Animal studies need enough subjects to answer the main question. Too few animals can miss a real effect. Too many animals can waste resources and raise ethical concerns. Power analysis helps balance both risks. It links the expected effect, natural variation, significance level, and desired power. The result gives a planned sample size before the protocol begins.
This calculator supports common planning designs. You can estimate one sample, paired measurements, two independent groups, two proportions, or a one way group comparison. It also supports unequal allocation. That matters when control animals are limited or treatment animals cost more. You can add attrition for loss, exclusion, mortality, or unusable samples. You can also add a design effect for clustering, cages, litters, strains, or repeated handling.
Choosing Reliable Inputs
Good inputs make better estimates. Start with a primary endpoint. Then define the smallest meaningful difference. Use pilot data, previous laboratory records, or published variance estimates. For continuous outcomes, the calculator can use raw means and a standard deviation. It can also use Cohen d. For binary outcomes, it can use two expected proportions or Cohen h. For several groups, it uses Cohen f as an approximate planning effect.
Alpha controls the false positive risk. A two sided test is common when effects may move either way. A one sided test can be justified only when the opposite direction is not meaningful. Power controls the chance of detecting the planned effect. Many protocols use eighty percent or ninety percent power. Higher power needs more animals.
Ethical Planning and Interpretation
Sample size is only one part of a strong protocol. Randomization, blinding, endpoint quality, and humane stopping rules also matter. Poor design can waste animals even when power looks adequate. Always document assumptions. Explain the chosen effect size. Record the variance source. Show the attrition allowance. Mention whether the calculation is per group or total.
The calculator rounds up because partial animals are impossible. It also reports adjusted counts after attrition and design effects. These numbers are planning estimates, not final scientific truth. Very small effects can create large sample needs. Very large pilot effects can be unstable. Sensitivity checks are useful. Try several plausible effect sizes. Compare eighty and ninety percent power. Review the burden on animals and staff.
Use the output as a structured starting point. Then confirm the method with a statistician, ethics committee, or institutional animal care group. This is especially important for complex models, repeated measures, survival endpoints, mixed effects designs, or regulatory submissions. Clear planning improves science. It also supports responsible animal use.
Checking Sensitivity
Run more than one scenario. Change the effect size slightly. Increase the standard deviation if data are uncertain. Raise attrition when procedures are demanding. Compare equal and unequal allocation. These checks show whether the plan is stable. They also reveal which assumptions drive the animal count most. Clearly.
FAQs
What does this calculator estimate?
It estimates animal sample size for planned studies. It uses power, alpha, effect size, allocation, attrition, and design effect to produce base and adjusted counts.
Can I use it for two animal groups?
Yes. Select two independent means for continuous outcomes. Select two independent proportions for binary responses, such as improved versus not improved.
What is desired power?
Power is the chance of detecting the planned effect when it truly exists. Common values are 0.80 and 0.90. Higher power usually needs more animals.
What alpha value should I enter?
Alpha is the false positive risk. Many studies use 0.05. Some confirmatory or regulatory studies may need stricter alpha values.
What is allocation ratio?
Allocation ratio is treatment animals divided by control animals. A value of 1 gives equal groups. A value of 2 gives twice as many treatment animals.
How is attrition handled?
The calculator inflates the base count by dividing through the expected retention rate. For 10% attrition, it divides by 0.90 and rounds up.
What is design effect?
Design effect increases sample size for clustering or dependence. Use it when animals are grouped by cage, litter, strain, site, or another shared source.
Can this replace a statistician?
No. It gives a planning estimate. Complex protocols, repeated measures, survival models, and mixed effects designs should be reviewed by a qualified statistician.
Why does the result round upward?
Animal counts must be whole numbers. Rounding upward protects the planned power and avoids underestimating the number needed for the study.
What effect size should I use?
Use the smallest meaningful biological difference. Support it with pilot data, published research, laboratory records, or a justified scientific rationale.
Is the group comparison exact?
The group comparison uses a planning approximation. It is useful for early estimates. Confirm final one way or complex models with specialized software.