help > RE: Correlation values and 2nd level effect size
Nov 28, 2015  04:11 PM | Alfonso Nieto-Castanon - Boston University
RE: Correlation values and 2nd level effect size
Dear Nicola and Pravesh,

Thank you Pravesh for the detailed response, and yes, Pravesh is exactly correct, the error bars in the ROI-to-ROI display represent 90% confidence intervals of the individual effects/regressors in your second-level model (basically on bar for each selected 'between-subjects effect' and 'condition' combination; e.g. if you are selecting two groups of subjects to perform a two-sample t-test the bar display will show two bars displaying the average connectivity within each group).

Also, to extract the pairwise correlation values, another approach in addition to what Pravesh described is to select your seed and target ROIs in that same ROI-to-ROI second-level results tab, and click on the 'import values' button. This will create new second-level covariates containing the connectivity values (typically Fisher-transfromed correlation coefficients) between your selected seed and target ROIs. You can use the 'export to file' option in Setup.CovariatesSecondLevel to export those values to a file if you want, or you can use Tools.Calculator to display or perform additional analyses on those values.

Hope this helps
Originally posted by Pravesh Parekh:
Hi Nicola,

I happened to check another random pair of ROIs in a different project and found that the error bars were corresponding to confidence interval in that particular case (confidence interval obtained after one sample t test). I think Dr. Alfonso would be able to clear it up...


Pravesh Parekh

Originally posted by Pravesh Parekh:
Hi Nicola,

I think I might be able to answer your question partially:

- I believe that the error bars indicate the quantiles (most likely the 0.25 and 0.75 quantile values).
As an example, take two ROIs. The ROI-ROI Fisher transformed correlation coefficients (for my data comprising of seven subjects) are:

y1 = 0.2677 ; -0.0862 ; 0.1108 ; 0.2222 ; 0.3000 ; 0.0448 ; 0.2750

The mean value is 0.1620 which is shown as my beta value in the results (0.16).

Now, if I were to calculate the quantiles of this set of data using the following MATLAB command:

quantile(y1, [0, 0.25, 0.5, 0.75, 1])

I get the following quantiles: -0.0862 ; 0.0613 ; 0.2222 ; 0.2732 ; 0.3000

Now, looking at the effect size graph (see attachment), I note that the blue area is the value from zero to 0.16 (the mean effect in my group) and the upper and lower error bar roughly correspond to 0.27 and 0.06 respectively (and hence the thought that the error bars correspond to these respective quantiles).

- When you right click on the second level results table, you get an option of exporting your stats which include the list of (mean) betas as seen in the table.

- Do explore the variable conn_*/results/secondlevel/ANALYSIS_01/Covariate_name/Condition_name/ROI.mat file. When you import this in MATLAB, you will have a structure with many fields. Some of note are:
y: would have the subject level betas
names: would have the source ROI names
names2: target ROI names
h: the effect size (mean beta)
F: the T stats value (or the stats mentioned in "statsname" entry)

From the ROI.h variable, you should be able to re-construct the Fisher transformed correlation coefficients and re-convert them to raw correlation coefficients (if you want) by using

r = tanh(z)

as suggested/discussed here: and here:


Pravesh Parekh

Originally posted by Nicola Toschi:
Hi Alfonso, hi List,

quick questions related to effect sizes: in 2nd level resolts (ROI to ROI) I can visualize a nice barchart displaying effect sizes (i.e. 2nd level regression coefficients). Related to this:

- What exactly do the error bars represent (confidence intervals)?
- Can the numerical coefficients (betas) be read or exported to file?
- Can I extract the pairwise correlation values (i.e. the dependent variables in the GLM)?

Thanks in advance!


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Nicola Toschi Nov 27, 2015
Pravesh Parekh Nov 27, 2015
Pravesh Parekh Nov 28, 2015
RE: Correlation values and 2nd level effect size
Alfonso Nieto-Castanon Nov 28, 2015
Nicola Toschi Feb 21, 2016