Statistical Non-Parametric Mapping

1. Statistical Non-Parametric Mapping

2. Limited assumptions are made about the distribution of your data. Uses your data to derive an idea of what can be expected of your data, and uses it to compute the probability of your findings. What does it mean to be “non-parametric”?

3. Why would I want to use non-parametric statistics? “Guaranteed valid” assumptions (Nichols, 2002) Not reliant on the Central Limit Theorem. (particularly useful with small degrees of freedom) i.e. false assumptions of normality at:

4. What can I test? H0: All conditions have the same effect. If all conditions are equal, then the labels should be interchangeable.

5. How can I get a p-value? As we reorder the images we find the maximal statistic (generally a t-statistic or pseudo t-statistic) for each combination of images.

6. Once we have a distribution of the maximum statistics, we can get the probability of finding a maximum statistic = each voxel within our grouping of interest, and get a adjusted p-value for each voxel. i.e. within this data there were 20 of 200 comparisons that yeilded t-values greater than or equal to t=6, that means the p-value at t=6 is ˜ .1 (This can work for the maximal cluster as well)

7. The statistical value that corresponds to the corrected .05 alpha level of interest is statistic that is greater than 95% of the maximal statistics found (similar to a threshold t-value).

8. Inaccurate estimates of variance? Since we can assume a certain amount of consistency of variance between neighboring voxels, it is justified to smooth the variance map (Nichols and Holmes 2001). If variance smoothing is implemented you will end up with a “pseudo t-statistic”

9. Non-parametric toolbox Developed by Andrew Holmes and Tom Nichols of University of Glasgow, and University of Michigan respectively.

10. What can I do with the toolbox? Primarily designed for PET and second level fMRI designs. Multiple and Single subject comparisons. i.e. Are these groups/conditions the same? Multiple and Single subject correlations. i.e. Does this variable correlate with each subjects brain activation?

11. What does the toolbox assume? Symmetrical Distributions for each condition. Exchangeability under H0 If all conditions are equal the labels should be arbitrary. Multi-subject anatomical equality. There is no discrimination between effects created by anatomical variation and experimental design.

12. Limitations… Lots of memory, and time. Computers have gotten faster since Holmes (1994) reported 8 hrs. processing time, but if you are working with big images, it may not work. If normality assumptions are found to be valid, then parametric statistics will prove more powerful.

13. Conclusion.