Statistical Parametric Mapping (SPM) is a method to create “Maps” of arbitrary statistical tests, which can be applied across the entirety of a continuous curve. These maps exist in the same dimensional space as their underlying data, which allows for the results to be more interpretable, as well as removing bias relating to selecting summary statistics like maximums, minimums or averages. Using random-field-theory, the inherent dependence between the parameters on these maps can be accounted for when determining how statistically relevant the results of a map are.

Statistical tests, such as a T-Test or ANOVA, are useful tools for determining statistical differences between group means, but are subject to limitations when applied to continuous data.

It is unclear at which point the test should be applied: whether that is the maximum value, 50% through the gait cycle, or some other point in time. When limiting the test to a single time point, the information outside of that time point is not included in the results.

This is the key benefit to using SPM: continuous statistical inference in the original space of the data, allowing for more insights and intuitive understanding of the results.

More detail on the mathematics behind SPM can be found on the page: The Math of Statistical Parametric Mapping

Sift provides a number of ways to visualize and interact with the results of SPM. An overview of all SPM visualizations is available on the Sift - Analyse Page

This page includes:

• Visualizing the maps;
• Visualizing the statistics;

Choosing your experimental hypothesis is very important, and this should influence the statistical test being undertaken. ANOVA provides us a broad look at all of our data: with the hypothesis that all groups have the same mean, we can easily test IF there is 1 or more groups not following this hypothesis, but we cannot discern which one it is. T-tests on the other hand can specifically tell us if any 2 groups are different, and specifically identify which tests are different.

For many groups, it is recommended to first use an ANOVA test, and if there is statistical differences, to use post-hoc t-tests with a bonferroni correction (or the Holm–Bonferroni method) to identify which group this is.

For related groups, it is recommended to use a paired t-test over a two-sample t-test, as it has strictly higher statistical power.

Step-by-step tutorials are available for SPM in Sift:

• SPM Tutorial.
• Analysis of Shoulder Angular Velocity between Elite Level and Average Collegiate Pitchers
• Effects of Fatigue During Basketball Free Throws Using SPM and ANOVA
• Impact of Shooting Arm Mechanics on Free Throw Accuracy Using PCA, K-Means, and SPM

Our implementation of Statistical Parametric Mapping is based on articles by Todd Pataky, as well as the textbook on the topic: “Statistical Parametric Mapping - The Analysis of Functional Brain Images”:

K. Friston, J. Ashburner, S. Kiebel, T. Nichols, and W. Penny, Statistical Parametric Mapping: The Analysis of Functional Brain Images, 1st ed.; Academic Press: Cambridge, MA, USA, 2006; ISBN 978-0-08-046650-7.

Pataky TC (2010) Generalized n-dimensional biomechanical field analysis using statistical parametric mapping. Journal of Biomechanics 43. 1976-82 ([1])