## Fall 2014: HS 851

#### Homework 4

Use the SOCR Neuroimaging dataset of visceral pain, irritable bowel syndrome, ulcerative colitis, and Crohn's disease.
• Problem 1: Is there evidence of hippocampal volume asymmetry in the IBS cohort? Formulate an appropriate research hypothesis, identify a suitable statistical technique, apply the corresponding software tool, and report your findings.
• Problem 2: Assume the gender distributions of the participants in this study accurately represents the 4 cohorts (Normals, IBS, Ulcerative Colitis and Crohn's disease). Let's say we wish to compare the proportions of males in the Normals and IBS groups. Use the Methods of Moments to compute estimates (p1 and p2) of the probabilities that a randomly selected male is from the asymptomatic normal control group (p1) and a randomly selected male is from the IBS control group (p2). Once you find the point estimates (p1 and p2), perform a statistical test to assess the differences between the proportions of males in the Normals and IBS groups. Note that you need to invert the conditioning: p'1=P(male|NC), and p'2=P(male|IBS). What is the confidence interval of the difference p'1 - p'2?
• Problem 3: Use the SOCR Fligner-Killeen test to investigate if the variances of the white matter volume (WMV) between the 3 cohorts (Normals, IBS, Ulcerative Colitis) are significantly different. Why is this important? Repeat this analysis looking for differences in the variability of the gray matter volume (GMV) in the controls group between genders. Elaborate on your fingings.
• Problem 4: Complete the following table, where patients indicates all study participant except the asymptomatic controls.
 Groups Patients Controls Total Female Male Total
Compute a point estimate and a 95% CI for the Odds Ratio of controls relative to gender. Next, apply the χ2 association test to investigate for association between participants' gender and diagnosis.

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