## Abstract Blood-oxygen-level-dependent (BOLD) activity can be described by its first and second order statistical properties. Typical studies analyze first order relationships between the BOLD time course and experimental condition--i.e., increases or decreases in BOLD activation are related to a particular experimental state. More recent fMRI studies have studied relationships involving second order statistics--i.e, the variance, or fluctuations in BOLD activation, were related to age, behavior, and behavioral performance. Despite these findings, statistical frameworks for modeling second order relationships have lagged behind frameworks for first order relationships. The dominant first order model, the General Linear Model (GLM), treats any fluctuation in BOLD activity as measurement noise and is therefore unable to detect experimentally related changes in BOLD variation. We introduce the Variance Design General Linear Model (VDGLM), a novel framework that facilitates the detection of variance effects. We designed the framework for general use in any fMRI study by modeling both mean and variance in BOLD activation as a function of experimental design. The flexibility of this approach allows the VDGLM to i) simultaneously make inferences about a mean or variance effect while controlling for the other and ii) test for variance effects that could be associated with multiple conditions and/or noise regressors. We demonstrate the use of the VDGLM in a working memory application and show that engagement in a working memory task is associated with whole-brain decreases in BOLD variance. ## Data The project uses data from the Human Connectome Project 1200 subjects release, which can be found [here](https://www.humanconnectome.org/). Our analyses begin with data from the [Minimal Preprocessing Pipeline](https://www.sciencedirect.com/science/article/pii/S1053811913005053). We run out anlaysis on 875 subjects that had low head motion. From the original grayordinate data, we extracted the time series for 333 surface regions of interest (ROIs) based on the [Gordon et al. atlas](https://academic.oup.com/cercor/article/26/1/288/2367115). Additionally, we performed scrubbing and motion correction. The data from the working memory task are stored in the file `tc_WM_875subj.mat.mat`. This file contains the following fields: motionX: estimated mean head motion for each subject and run readme: short readme subjs: subject ids tasks: run ids tc: timecourse for each subject and run The files `design_WM_LR.mat` and `combdesign_WM_LR.mat` contain the corresponding uncombined (10 conditions) and combined (4 conditions) design matrices, respectively. Each file contains the fields: conditions: condition labels rst: a structure that contains variables describing the time series. rst.mtx is the design matrix. ## Code All relevant code for performing analyses can be found [here](https://github.com/geebioso/VDGLM). Please note that this repository is not production level code nor designed to run on public computers, but is instead provided to illuminate details of our analyses.