Edge-level Statistical Tests

Methods

The non-permuted method calculates the correlation of each Region Of Interest (ROI) to all other ROIs via the given test. These results are stored as a correlation coefficient, coeff, a p-value, prob, and a thresholded p-value, prob_sig. The permuted method is identical except the variables have a _perm suffix.

Common Inputs

P:

Edge-level p-value threshold

Network Atlas:

Network Atlas

Functional Connectivity:

Initial correlation matrix (r-values or Fisher z-transformed r-values) of size NROIs x NROIs x Nscans

Behavior:

MATLAB table (.mat) or tab separated text file (.txt)

Variable Name

Next Variable Name

More Variable…

1

5

1.5

0

1

3

1

7

2.6

…

…

…

Each column header is a name of a variable. Each column contains Nscans entries. After loading this file, the table should display in the GUI. The user may mark one column as ‘Behavior’ for the score of interest. Other columns may be marked as ‘Covariates’ which are partialed prior to running statistics.

Note: Network Level Analysis cannot handle missing values for behavior or covariates. If there are NaNs or missing values in a column, using this column will result in errors

Provided Tests

  • Pearson’s r

    • MATLAB corr function with (type, Pearson)

  • Spearman’s \(\rho\)

    • MATLAB corr function with (type, Spearman)

  • Spearman’s \(\rho\) estimator

    • Faster approximation of the Spearman’s rho function at the cost of slightly less accurate result.

    • Based on developer testing, rho values may differ by \(10^{-4}\) and p-values by \(10^{-5}\).

    • This error is passed on to the network-level tests, and can cause p-value difference by \(10^{-4}\)

    • These differences were found with 10,000 permutations. Less permutations results in higher error in a less evenly distributed fashion.

    • This is recommended for exploratory research with the Spearman’s rho function for publications

  • Kendall’s \(tau\) -b

    • Implements Kendall’s \(\tau\) -b using C code in a MATLAB MEX file (+mex/+src/kendallTauB.c)

    • Faster implementation that standard MATLAB code providing identical \(\tau\) and p-values.

    • Run-time difference from O(n2) to O(n log n)

    • This is done with a red-black tree.

  • Welch’s t -test

    • Implements an optimized Welch’s t-test comparing the functional connectivity of two groups.

    • FC for both groups must be concatenated along the 3rd dimension (Nscans). As such, the third dimension will be Nscans x 2

    • Behavior must contain Group IDs for both groups. The simplest way to do this is by creating a column vector containing 0’s for subjects in Group 1 and 1’s for subjects in Group 2.

    • We also recommend using that same column for setting the Permutation Groups as described in (link to �Setting Permutation Groups� here).

    Group name(s):

    Names associated with each group. (For example, ‘Male’ and ‘Female’)

    Group val(s):

    Behavioral value associated with each group. If ‘Female’ is denoted as ‘0’, and ‘Male’ as ‘1’, set the vals to the numerical values.

  • Paired t -test

    • MATLAB ttest function with (Dim, 2)

    • Otherwise implemented the same way as the Welch’s t-test above

  • Pre-calculated data loader

    • Allows loading of observed and permuted edge-level data the user has pre-calculated outside the NLA.

    • Four .mat files needed as inputs

    • p-values should be thresholded

    Observed p:

    .mat file containing NROI_pairs x 1 matrix of logical values, the observed, thresholded edge-level p-values. NROI_pairs are the lower triangle values of a NROIs x NROIs matrix.

    Observed coeff:

    .mat file containing NROI_pairs x 1 matrix of observed edge-level coefficients.

    Permuted p:

    .mat file containing NROI_pairs x Npermutations of logical values. Observed, thresholded, permuted p-values.

    Permuted coeff:

    .mat file containing NROI_pairs x Npermutations of permuted edge-level coefficients.