#### Homework 3

Use the

SOCR Neuroimaging dataset of visceral pain, irritable bowel syndrome, ulcerative colitis,
and Crohn's disease.

**Problem 1**: Investigate the effect of the grouping (Group), separating the 3 cohorts, on the
gray matter brain volume (GMV), i.e., you can take group as a categorical variable and the
GMV values as the observations. Use the
SOCR 1-Way ANOVA applet, or
R to carry the
calculations. Provide all results and explicitly state your inference.
**Problem 2**: Use
2-way ANOVA (using *gender* and *group* as the 2 factors) on the
*R_insular_cortex* volume (insular shape has been reported to be associated with visceral pain, irritable bowel syndrome,
and ulcerative colitis). Repeat the analysis using the counterlateral *L_insular_cortex* volume.
Report your findings and interpret the results.
**Problem 3**: Determine a
linear model of association between the the response (Total Brain Volume, TBV)
and the following predictors (Group, Sex, and Age). Explain your findings and interpret
your model results.
**Problem 4**: Do people with larger brains necessarily have bigger
hippocampal volumes (e.g., L_hippocampus + R_hippocampus)? Formulate a research hypothesis,
propose an appropriate statistical technique, apply the corresponding software tool, and
report your findings.