There is no threshold for correlation values which says they are insignificant or "mathematically irrelevant", only statistical tests can tell you if something is unlikely to be due to chance. The fact that a small r-value is statistically significant just means that the r-values if there was no effect are even closer to zero. Yes, the *correlations* are small (which is not a true measure of effect size, it is highly dependent on SNR), but it is consistent. Matt was explaining why you should not expect the correlation values to *ever* be large in any high-resolution BOLD data.
fMRI BOLD scans do not have much SNR, each voxel's timeseries is dominated by random noise, this is why you need a lot of timepoints, and use correlation (or similar things like GLM for task). However, the MR physics seems to work out such that when you use large voxel sizes (low resolutions), you get all of the signal "within" that voxel, while all the independent noise coming from "within" that voxel all gets averaged together, and therefore doesn't add up to much. Thus, if you are used to large-voxel data (or if you are used to doing a lot of smoothing, which has similar effects), you may expect per-voxel correlation values that are rather larger than 0.05. However, in HCP data, we acquire smaller voxels, resulting in less signal per voxel, while the noise within the voxel isn't "averaged" over as much volume, and thus the per-voxel timecourse is more dominated by random noise. However, since random noise has expected covariance of 0 with other noise, this isn't an issue for finding statistically robust effects as long as you have enough timepoints. However, correlation is not trying to find the effect size - in particular, it divides by the *total* standard deviation of the timeseries (which is basically equal to the standard deviation of the noise, because of how much noise dominates in BOLD data), while only the signal of interest adds to the numerator. Thus, with less signal *per voxel* with high resolution scans, you get lower correlation values *per voxel*. This is expected, but not really meaningful - really, it just means that your signal is divided up into smaller spatial units, and your noise also (which is exactly what it means to have higher resolution data). If you smoothed the data to be more like low-resolution data, your correlation values would increase, since the noise standard deviation would decrease (but smoothing like this is not a good idea since you lose spatial localization - as I said, a low correlation value doesn't mean that something is due to chance, that is for statistical tests to decide). Tim On Tue, Jul 10, 2018 at 5:54 AM, Amin Dadashi <[email protected] > wrote: > Thank you Matthew. To be more accurate, my question is about the expected > r-values indicating an existing connectivity between brainstem ROI to the > cortical areas. I have not seen many articles reporting the values of the > significant correlation coefficients and so I am wondering why it is not > considered to be important. > > In my case, I have found significant connectivity from the specific > brainstem ROIs, but looking at the peak significant r-values, they are not > exceeding 0.05. From the mathematical point of view, such a small r-value > means the two compared variables are irrelevant; at the same time, it is > not possible to ignore that the cortical pattern of these significant > mathematical irrelevance seem to be meaningful. I believe that I am missing > a point, where your expert opinion might help me to figure out. > > Thanks a lot, > Amin > > > > On Mon, Jul 9, 2018 at 10:48 PM, Glasser, Matthew <[email protected]> > wrote: > >> There is more unstructured noise in HCP data because of small voxel size >> and fast TR. Basically that means the ratio between the neural signal and >> the random noise is lower and that leads to lower correlation coefficients. >> >> >> Peace, >> >> Matt. >> >> From: <[email protected]> on behalf of Amin Dadashi < >> [email protected]> >> Date: Monday, July 9, 2018 at 4:14 AM >> To: hcp-users <[email protected]> >> Subject: [HCP-Users] Brainstem to cortex baseline r-value >> >> Dear HCP users, >> >> Recently, I have tried to calculate the zero-order correlation between >> some brainstem ROIs and the cortical vertices. Looking at the mean >> subjects' correlation map, the connectivity pattern totally makes sense. >> Even after doing the statistical testing (using permutation based on >> maximum t-statistics) the significant correlated clusters are located in >> the expected areas. However, the magnitude of the correlation coefficients >> are very small (in the order of 0.05 for the peak vertices in the mean >> map). I have also done the volume-based voxel-wise analysis for the same >> brainstem ROIs and I had similar findings there. >> Is there any explanation for such small r-values even though the >> significant correlations seem to be meaningful? >> >> Thank you all, >> Amin >> >> _______________________________________________ >> HCP-Users mailing list >> [email protected] >> http://lists.humanconnectome.org/mailman/listinfo/hcp-users >> >> >> ------------------------------ >> >> The materials in this message are private and may contain Protected >> Healthcare Information or other information of a sensitive nature. If you >> are not the intended recipient, be advised that any unauthorized use, >> disclosure, copying or the taking of any action in reliance on the contents >> of this information is strictly prohibited. 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