Power and Sample Size Calculation for Neuroimaging Studies

 By Satoru Hayasaka



How many subjects do we need to scan in our study? This is one of the most frequently asked questions among neuroimagers writing a research proposal. The answer lies between the following two paradoxical facts. It is important to include a sufficiently large number of subjects to detect the signal or effect of interest. At the same time it is also important to include as few subjects as possible to reduce the overall cost of a study. To address this issue, in this project, we develop a tool for determining the number of subjects needed in neuroimaging studies.

Our power calculation method is based on random field theory (RFT), the method which has been used in SPM (statistical parametric mapping)-type analyses of neuroimaging data. Compared to existing methods, our approach has some advantages:

  • Power calculation accounts for multiple comparisons, controlling family-wise error (FWE) rate.
  • Considerably faster, requiring only a few minutes at most.
  • Power and sample sizes can be calculated from a pilot data set even with a small number of subjects.

As part of this project, we are working on the following aims:

  • Developing YottaWatt, a power calculation tool for neuroimagers
  • Meta-power analysis
  • Power calculation framework for FDR-correction


A power calculation tool for neuroimagers
We are in a process of producing a user-friendly power calculation tool for neuroimaging studies called YottaWatt. Please check this page regularly for any update on our progress in the software tool. This is named after the largest SI unit for power. One YottaWatt equals 1024 Watts. We anticipate the beta-version of YottaWatt tool to be available later in 2009. Please check this page regularly for any update on our progress in the software tool.

Here are some examples of power and sample size calculation results produced by YottaWatt. These examples are based on a pilot data set (N=5) of an auditory fMRI experiment. In particular, these results demonstrate power and sample size required to detect activations associated with hearing white noise relative to silence in a block design experiment.

 Power curves

If the location and the effect size of anticipated signals are known, then power curves can be generated.


Power maps

Power maps can be useful in visualizing how sensitivity varies in different areas of the brain.


Sample size maps

Sample size maps can also be a useful study planning tool. These maps help investigators determining how many subjects are needed to detect signals in different areas of the brain.

Meta-Power Analysis
Another goal in our power map project is to assess how accurate our power calculation method is. To facilitate this process, we are generating gold-standard power maps from some functional and structural MRI study data. The concept is quite similar to famous Desmond & Glover paper (J NeuroSci Method 118: 115-128, 2002), but instead of simulated data, we plan to use actual brain imaging data. By repeatedly sampling from the actual data set and determining the proportion of detecting signals at each voxel, we can estimate the true statistical power map.

The resulting gold-standard power maps can serve as a point of reference for quality control for the YottaWatt tool. At the same time this will be the first study of its kind assessing statistical power of various studies retrospectively.

Power for FDR-Corrected Tests
In addition to power for FWE-corrected tests, we are also developing a framework for power calculation for FDR (false discovery rate). The FDR-correction controls the proportion of false positives out of all activated voxels, yielding more statistical power compared to the FWE-method. We plan to implement power calculation for FDR-based tests in our YottaWatt tool as well.


Conference Proceedings

This work was presented at the Human Brain Mapping Conference in Chicago in June, 2007.

  • Hayasaka S, Peiffer AM, Hugenschmidt CE, Laurienti PJ. Power and Sample Size Maps for Neuroimaging Studies by Non-Central Random Field Theory. Poster (PDF 748KB) or PowerPoint Slides (PDF 951KB)

This work, outlining statistical power on FDR-corrected tests, was presented at the Fifth International Imaging Genetics Conference at University of California, Irvine in January, 2009.

  • Hayasaka S. Statistical Power in Combined Whole-Brain Whole-Genome Association Studies. Poster (PDF 734KB)


Also a paper describing our methods is available.

 Technical report

For those interested, the details on derivation of the non-central random field results are available in this technical bulletin.


This project is supported by the National Institute of Neurological Disorders and Stroke (NS059793).

Comments / Questions

If you have any comments or questions, please let me know by e-mail at shayasak@wfubmc.edu.