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Analysis ‐ Data
Statistics should be presented: statistic (degrees of freedom) = value; P = value; effect size statistic = value; and per cent confidence intervals = values
t-tests, correlations, partial correlations, ANOVAs, MANOVAs,… are just specific instances of the linear model.
Parametric statistical models are assumed at each voxel, using the general linear model to describe the data variability in terms of experimental and confounding effects, with residual variability. Hypotheses expressed in terms of the model parameters are assessed at each voxel with univariate statistics.
Is commonly used for dimension reduction. An usage tutorial can be found on scikit website. In this study we developed multiple PCA metrics:
Statistical significance of the LVs is determined via permutation testing. permutation sample: In a permutation test, a new data set, called a permutation sample, is obtained by randomly reordering the rows (i.e., observations) of X and leaving Y unchanged. The PLSC model used to compute the fixed effect model is then recomputed for the permutation sample to obtain a new matrix of singular values. This procedure is repeated for a large number of permutation samples, say 1000 or 10,000. The set of all the singular values provides a sampling distribution of the singular values under the null hypothesis and, therefore can be used as a null hypothesis test.
Bootstrap resampling is used to examine the contribution and reliability of the input features to each LV.
Split-half resampling can optionally be used to assess the reliability of the LVs.
A cross-validated framework can optionally be used to examine how accurate the decomposition is when employed in a predictive framework.
Fixed vs random effects