Small boat navigating stormy seas, representing challenges of small pilot studies in research.

Pilot Study Pitfalls: Are Small Samples Derailing Your Research?

Soraya Malik in Mind & Education August 2025 • 4 min read.

"Unlock the secrets to smarter experimental design and avoid common statistical traps when working with limited data."

In experimental design, researchers often rely on pilot studies to refine their approach before launching larger investigations. The conventional wisdom assumes that access to large pilot studies is a given, but what happens when resources are limited, and pilot studies are small? This situation can introduce unexpected pitfalls, particularly when using the Neyman Allocation method, a popular technique for optimizing sample allocation.

The Neyman Allocation is designed to minimize the variance in estimates of the Average Treatment Effect (ATE). It works by allocating more units to the group with greater outcome variability, assuming you know the standard deviations. However, in practice, these variances are often estimated from pilot studies. The challenge arises when these pilot studies are small, leading to inaccurate variance estimates and potentially derailing the entire experimental design.

This article explores the performance of the Neyman Allocation method when pilot studies are small, highlighting how this can actually increase the asymptotic variance of ATE estimates compared to simpler methods like balanced randomization. We will discuss scenarios where this is most likely to occur and provide strategies to navigate these challenges, ensuring your research remains robust even with limited pilot data.

When Does the Neyman Allocation Go Wrong?

Small boat navigating stormy seas, representing challenges of small pilot studies in research.

The Neyman Allocation, while powerful in theory, relies on accurate estimates of variance. When pilot studies are small, these estimates become unreliable, leading to suboptimal allocation. Specifically, the Neyman Allocation can perform worse than balanced randomization when outcomes are relatively homoskedastic (i.e., variances are similar across treatment and control groups) or when outcome variables exhibit high kurtosis (heavy tails).

Homoskedasticity undermines the core principle of the Neyman Allocation, which is to allocate more units to the group with higher variability. When both groups have similar variance, a balanced allocation often provides more stable and accurate results. High kurtosis, on the other hand, makes variance estimation difficult, even with larger samples. In small pilot studies, heavy-tailed distributions can lead to extreme variance estimates that drive the Neyman Allocation toward inefficient or even counterproductive allocations.

Homoskedasticity: Occurs when the variance is consistent across all groups.
High Kurtosis: When a distribution has fat tails (extreme values).

To illustrate the practical implications, consider a scenario where a researcher is evaluating a new educational intervention. If the pre-existing performance levels (outcome variable) are similar between the treatment and control groups, or if there are many outliers, using the Neyman Allocation with a small pilot study might lead to a less efficient experimental design than simply assigning an equal number of participants to each group.

Navigating the Pitfalls

Working with small pilot studies requires caution, but it doesn't mean abandoning optimization altogether. Instead, researchers should consider alternative strategies such as testing for homoskedasticity before applying the Neyman Allocation or using regularization techniques to stabilize variance estimates. By understanding the limitations and potential pitfalls of the Neyman Allocation in small samples, you can make informed decisions to safeguard the validity and reliability of your research outcomes.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2206.04643,

Title: On The Performance Of The Neyman Allocation With Small Pilots

Subject: econ.em

Authors: Yong Cai, Ahnaf Rafi

Published: 09-06-2022

Everything You Need To Know

What is the Neyman Allocation and why is it used in experimental design?

The Neyman Allocation is a statistical method used in experimental design to optimize the allocation of experimental units (e.g., participants) to different treatment groups. Its primary goal is to minimize the variance in estimates of the Average Treatment Effect (ATE). This is achieved by allocating more units to the group with greater outcome variability, which allows for more precise estimates. However, this method relies on accurate estimates of standard deviations, making it vulnerable when these estimates come from small pilot studies.

How can small pilot studies negatively impact research outcomes when using the Neyman Allocation?

Small pilot studies can lead to inaccurate variance estimates, which are crucial for the Neyman Allocation. The Neyman Allocation can perform worse than balanced randomization when using estimates derived from small pilot studies. When the estimated variances are incorrect, the allocation of units becomes suboptimal. This can result in less efficient experimental designs and less reliable estimates of the Average Treatment Effect (ATE). This means the allocation may not effectively minimize variance, leading to less precise and potentially misleading results.

What are homoskedasticity and high kurtosis, and how do they affect the Neyman Allocation?

Homoskedasticity refers to the condition where the variance is consistent across all groups being studied. When outcomes exhibit homoskedasticity, the Neyman Allocation, which is designed to allocate more units to groups with higher variability, becomes less effective because it doesn't have a clear target. High kurtosis describes distributions with fat tails (extreme values). In small pilot studies, high kurtosis makes variance estimation very difficult, leading to unreliable estimates that can drive the Neyman Allocation toward inefficient or counterproductive allocations. Both scenarios undermine the assumptions underlying the Neyman Allocation.

In what scenarios might balanced randomization be a better choice than the Neyman Allocation, especially with small pilot studies?

Balanced randomization, where an equal number of participants are assigned to each group, can be a better choice than the Neyman Allocation in specific scenarios, particularly when dealing with small pilot studies. This is especially true when the outcomes are relatively homoskedastic (similar variances across groups) or when the outcome variables exhibit high kurtosis. In these situations, the Neyman Allocation, which relies on accurate variance estimates, may lead to less efficient designs than the simpler balanced approach. This is because the Neyman Allocation is less effective when the differences in variability are small or when the data is highly skewed.

What strategies can researchers employ to mitigate the risks associated with using the Neyman Allocation with small pilot studies?

Researchers can adopt several strategies to safeguard the validity and reliability of their research when using the Neyman Allocation with limited data. One approach is to test for homoskedasticity before applying the Neyman Allocation. If the variances are similar across groups, balanced randomization might be a more appropriate choice. Another strategy is to use regularization techniques to stabilize variance estimates. These techniques help to prevent extreme estimates that can skew the Neyman Allocation. By understanding these limitations and potential pitfalls, researchers can make informed decisions to improve the robustness of their research outcomes.