The Resource Equation Method for Animal Sample Size

The resource equation method is a quick, defensible way to size a small animal experiment when a full a priori power calculation genuinely is not feasible — not a shortcut around one. It gives an experimental-unit count from a single arithmetic check, with no need for a prior estimate of effect size or variance. Used where it fits, an IACUC can accept it as a legitimate justification. Used to dodge a calculation that real preliminary data would support, it is a rigour problem that a competent reviewer — and increasingly, a journal editor checking ARRIVE 2.0 compliance — will catch.

The formula

Festing and Altman set out the method in their widely cited 2002 ILAR Journal paper on the design and statistical analysis of laboratory-animal experiments. The calculation itself is a single subtraction:

E = Total number of animals − Total number of experimental groups

E is the “error degrees of freedom” in the underlying analysis of variance — the number of residual degrees of freedom left over once group means have been estimated. As a worked example: a study with 4 treatment groups and 8 animals per group uses 32 animals total, giving E = 32 − 4 = 28. A study with 3 groups and 6 animals per group gives E = 18 − 3 = 15.

The conventional target, per Festing and Altman and repeated in Charan and Kantharia’s frequently cited 2013 summary in the Journal of Pharmacology & Pharmacotherapeutics, is E between 10 and 20. Below about 10, the design is under-powered to detect a real ANOVA effect with reasonable precision; above about 20, additional animals are unlikely to meaningfully sharpen the estimate, so more E adds ethical and resource cost without buying real statistical value. If E is well below 10, the fix is normally to add animals per group (not more groups, which does little to E on its own) or reduce the number of groups to a design that answers the same question more efficiently.

When the resource equation method is genuinely the right tool

The method exists for a specific, real situation: early-stage or exploratory work where the researcher has no defensible basis for the inputs a proper power calculation needs — an estimate of effect size, an estimate of the outcome’s variance, and a chosen significance level and power. That situation is common and legitimate in animal research, not a sign of poor planning:

• First-in-model pilot work, where no prior data exist for this specific strain, procedure, or endpoint combination, and a pilot study’s own stated purpose is generating the variance estimate a later power calculation will need.
• Genuinely exploratory studies with multiple endpoints or a complex analytical design, where no single effect size can meaningfully anchor a power calculation and the study is not testing one pre-specified hypothesis.
• Novel models or procedures for which the published literature offers nothing comparable to draw a variance estimate from, and generating that estimate is legitimately part of what the study is for.

In each of these, treating the resource equation’s 10–20 range as “enough animals to get a usable signal without wasting subjects” is an honest, proportionate justification. It is also, by design, a much weaker constraint than a power calculation — which is exactly why it stops being appropriate once the missing inputs are actually available.

When a proper a priori power calculation is expected instead

The resource equation method was never meant to replace formal power analysis where power analysis is possible. Festing and Altman’s own guidance frames it as a fallback for situations where the assumptions a power calculation needs cannot be met — not as a general-purpose alternative. A proper a priori calculation, using an estimated effect size and variance (from pilot data, the published literature, or a closely comparable prior study), a stated significance threshold, and a target power, is expected whenever those inputs genuinely exist. That is the case for:

• Any confirmatory study — one designed to test a specific, pre-registered hypothesis rather than generate one, where the whole point of the sample size is controlling the risk of a false-negative result at a stated power.
• Any study for which comparable prior data exist — a previous study using the same model, a closely related published dataset, or the study’s own pilot phase — since an effect-size estimate is then available and there is no principled reason not to use it.
• Work heading toward regulatory submission or publication in a journal that checks ARRIVE 2.0 compliance, where sample-size justification is one of the ten minimum Essential 10 reporting items, not an optional extra.

This is also increasingly the default IACUC expectation, not just a statistical nicety. A protocol that reaches for the resource equation method where a real effect-size estimate was available — because it is easier to state, or because it tends to justify a smaller, cheaper cohort — is a weaker scientific justification masquerading as a simpler one, and reviewers experienced with the method recognize the pattern. Reduction, the “R” this method is most often invoked to serve, means using no more animals than the study needs to answer its question reliably — not fewer than that. An E of 10–20 arrived at by convenience rather than genuine data absence does not satisfy Reduction; it just moves the risk of an inconclusive, uninterpretable, and ultimately animal-wasting result from the planning stage to the results stage, where it costs the same animals for a worse scientific answer.

What an IACUC should look for in the sample-size justification

Reviewing this section of a protocol is a judgment call about which method fits the study, not a check that a number was calculated at all. A reviewer should confirm:

• The stated rationale for the chosen method actually matches the study’s design — a confirmatory hypothesis-testing study justified only by E falling in the 10–20 range, with no explanation for why a power calculation could not be done, is the pattern most worth questioning.
• Where a power calculation is used, its inputs are sourced and stated — the effect size, variance estimate, alpha, and target power, with a citation to where each estimate came from (pilot data, prior literature), not just a final animal number.
• Where the resource equation is used, the reason a power calculation was not feasible is actually stated — “no prior data exist for this endpoint in this model” is a real justification; an unexplained choice of the simpler method is not.
• The number of experimental groups and the per-group N are both given explicitly, so E can be checked directly rather than taken on trust, and so the experimental unit is unambiguous — the resource equation, like a power calculation, only means what it claims to mean if animals, not measurements or litters, are the unit being counted.

This mirrors the general animal-protocol review standard set out in the Guide for the Care and Use of Laboratory Animals: the committee’s job is to confirm the number of animals proposed is the number the science actually requires, using whichever justification method the study’s own data situation supports — and to push back when the method chosen looks selected for convenience rather than fit.

A related, sharper tool: sensitivity power analysis

When neither a full a priori power calculation nor the resource equation feels like the right fit — for example, when the total N is effectively fixed by cost, animal availability, or a prior ethical ceiling, and the real question is what effect size that fixed N can actually detect — a sensitivity power analysis answers a different, often more honest question: given this many animals, what is the smallest effect this study is capable of finding at the stated power? That reframing is frequently a better fit for constrained animal work than either the resource equation or a forward power calculation with a guessed effect size, and it produces a number an IACUC or reviewer can sanity-check on its own terms.

Frequently asked questions

Is E = 10–20 a hard regulatory requirement?

No. It is a widely followed methodological convention from Festing and Altman’s guidance, not a figure written into the Animal Welfare Act, PHS Policy, or Directive 2010/63/EU. An IACUC or ethics body can and does apply judgment around it — the range is a rule of thumb for where additional animals stop buying meaningful precision, not a pass/fail threshold.

Can the resource equation method be used for a confirmatory, hypothesis-testing study?

It can be stated, but it is the wrong tool if a defensible effect-size and variance estimate is actually available — in that situation reviewers and journals following ARRIVE 2.0 expect a proper a priori power calculation, and using the resource equation instead reads as avoiding a stricter test the data could have supported.

What counts as “total number of groups” when a study has multiple factors?

Every distinct treatment combination in the design counts as one group for this calculation — a 2×2 factorial design has four groups, not two, even though it varies only two factors.

Does a higher E always mean a better-justified study?

No — past roughly 20, additional animals add ethical and resource cost without a correspondingly useful gain in precision for this method’s purposes. The resource equation is explicitly a range, not a “more is better” scale, which is part of why it maps onto Reduction rather than against it when used appropriately.

Where can I read the original methodology?

Festing MF, Altman DG. “Guidelines for the design and statistical analysis of experiments using laboratory animals.” ILAR Journal. 2002;43(4):244–258. A concise, frequently cited summary of the same method is Charan J, Kantharia ND. “How to calculate sample size in animal studies?” Journal of Pharmacology & Pharmacotherapeutics. 2013;4(4):303–306.