Minimal Effect of Interest

When planning a study, you need to specify an effect size to calculate the required sample size. The most defensible way to do this is to define the minimal effect of interest — the smallest effect that would be scientifically or practically meaningful to detect.

This is sometimes called the smallest effect size of interest (SESOI). Whatever the name, the principle is the same: decide in advance what difference would matter, and power your study to detect it.

Why not just use the effect size from prior literature?

Using an effect size from a published study is common but has significant problems:

Published effects are systematically overestimated due to publication bias. Studies with small or null effects are less likely to be published, so the literature skews toward larger effects.
The effect size from one study reflects one sample, one protocol, and one measurement instrument. It may not apply to yours.
Powering a study to detect an effect that turns out to be inflated means the study will be underpowered for the true effect.

Defining your own minimal effect of interest reduces over-reliance on published point estimates. Prior literature can still inform your choice, but it should not replace your judgment about what difference would actually matter in your study.

How to define a minimal effect of interest

There is no single method. The following approaches are commonly used in life sciences research:

From clinical or biological relevance Define the smallest difference that would change a decision or interpretation. For a biomarker study, this might be the change that crosses a diagnostic threshold. For an in vivo experiment, it might be the effect size that would justify proceeding to the next stage of validation.

Ask: if the true difference is smaller than this, would the result still matter? If the answer is no, that threshold is your minimal effect of interest.

From measurement precision Consider what the measurement process can reliably resolve. If your minimal effect is far smaller than assay precision or measurement variability, it may be difficult to estimate or interpret in practice. In general, the minimal effect of interest should be meaningfully larger than the noise floor of the measurement process.

From field conventions Some fields have established conventions for what constitutes a meaningful difference — for example, a specific percentage change in cell viability, a fold-change threshold in gene expression, or a clinically meaningful difference score for a patient-reported outcome. These are starting points, not replacements for your own judgment.

Converting to a standardized effect size

Power calculations in Licklider use standardized effect sizes: Cohen's d for t-tests, Cohen's f for ANOVA, and Cohen's w for chi-square.

If you have defined your minimal effect of interest in raw units — for example, a 10-point difference on a continuous scale — you need to convert it to a standardized effect size before entering it into the power calculation.

Cohen's d from a raw difference:

d = Δ / SDpooled

where Δ is the minimal raw difference and SDpooled is the expected pooled standard deviation across groups. Use pilot data or published variability estimates for SDpooled.

Cohen's f from Cohen's d (two-group case):

f = d / 2

For ANOVA with more than two groups, f depends on the pattern of group means, not just pairwise differences. Consult a power analysis reference for multi-group calculations.

Licklider does not infer that multi-group mean pattern for you on this page. If your design has more than two groups, you need to decide what configuration of group means represents the smallest meaningful pattern before entering f.

What this choice feeds into

This page is about choosing the planning input, not about returning the final sample-size answer by itself. In Licklider, the MEI decision feeds the effect-size field used by the Power Analysis and Sample Size workflow.

Once you enter a standardized effect size there, Licklider returns the required sample size and the achieved power for the selected design. The exact output depends on the test family:

Independent-samples t-test: required n per group
Paired t-test: required n as pairs
One-way ANOVA: required n per group
Chi-square: required total n

This means the practical output of a good MEI choice is not a p-value or figure on this page. It is a more defensible required-sample-size target in the linked power workflow.

Using MEI in Licklider

When running a power analysis in Licklider, enter your standardized effect size in the effect size field of the Power panel. If you have defined a minimal effect of interest and converted it to Cohen's d, f, or w, use that value here.

Licklider does not automatically convert a raw difference into d, f, or w for you on this page. In particular, it does not choose SD_pooled, decide which literature estimate is credible, or infer the multi-group mean pattern needed for ANOVA with more than two groups. Those are design judgments that should be made explicitly before you treat the resulting sample size as claim-bearing.

This is the most defensible approach: the required sample size is determined by what difference you care about, not by what a previous study happened to find.

For a full description of the power calculation inputs and outputs → see Power Analysis and Sample Size.

If you instead use an observed effect from a small pilot dataset, Licklider can run the calculation in the power workflow, but this page should still be read as a warning that unstable or inflated inputs will give unstable or inflated sample-size targets.

A note on direction

The minimal effect of interest is a magnitude, not a direction. Whether your hypothesis is directional is a separate planning question. In the current Licklider power workflow, t-test power calculations are two-sided by default; hypothesis direction is documented separately.

For more detail → see Hypothesis Direction and Sidedness.

What this page does not cover

Running the power calculation itself → see Power Analysis and Sample Size
Setting hypothesis direction → see Hypothesis Direction and Sidedness
How effect size is reported in results → see Effect Size, CI, and N Reporting

Design Rationale & References

Licklider's design choices

Licklider frames MEI as the preferred starting point for power planning because the planning target should come from the smallest effect that would matter scientifically, not from whichever published estimate happens to be largest or easiest to find. That reduces over-reliance on a literature that is often distorted by publication bias [1]. The page also requires the user to convert raw effects into standardized inputs such as d, f, or w because power formulas operate on those standardized scales, and the right conversion depends on design-specific quantities that Licklider should not guess for the user [3].

The boundary is deliberate: Licklider helps you carry a justified MEI into the power workflow, but it does not pretend to know what your assay precision, decision threshold, or scientifically meaningful difference should be. Those are protocol choices, not UI defaults. In that sense, the page is designed to prevent false precision rather than automate judgment [2].

Methodological foundations

Ioannidis, J. P. A., & Trikalinos, T. A. (2007). The empirical implications of publication bias. The Lancet, 370(9587), 445-446.
→ Supports the warning that published point estimates are often inflated and should not be treated as neutral planning targets.
Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence Tests: A Practical Primer for t Tests, Correlations, and Meta-Analyses. Social Psychological and Personality Science, 9(4), 355-362.
→ A practical reference for specifying a smallest effect size of interest in advance rather than backing into interpretation after the data are collected.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
→ Classical reference for standardized effect size parameterizations such as d, f, and w, which are the scales used in the linked power workflow.

Implementation boundaries

This page explains how to choose the effect-size input for power planning; it does not itself return a required sample size.
Licklider does not automatically decide the minimal meaningful raw difference, the expected SD_pooled, or the multi-group mean pattern needed to derive f for ANOVA with more than two groups.
If you bring in an effect size from prior literature or a small pilot sample, Licklider can use it in the power workflow, but it cannot determine whether that estimate is inflated, transportable, or appropriate for your protocol.
The page does not promise automatic correction for publication bias or automatic conversion from every raw scientific scale into the standardized effect size required by each test family.