Many people suffer back or neck pain due to bulging discs in the lumbar or cervical spine, but the thoracic spine (the section inbetween) is less well-studied. The article “Kinematic analysis of the space available for cord and disc bulging of the thoracic spine using kinematic magnetic resonance imaging (kMRI)” (The Spine J. 2018: 1122–1127) describes a study using kMRI to measure disc bulge (mm) in neutral, flexion, and extension positions. 

a. Suppose measurements were taken on just 6 subjects. The following bulge measurements at the T11–T12 disc (bottom of the thoracic spine) are consistent with information in the article:

Convert these measurements into withinblock ranks, and use the Friedman test to determine if the true average disc bulge at T11–T12 varies by position.
b. The study actually involved 105 subjects, each serving as her/his own block. The sum of the ranks for the three positions were neutral = 219, flexion = 222, extension = 189. Use these to perform the Friedman test, and report your conclusion at the .05 significance level.
c. Similar measurements were also taken on all 105 subjects at the T4–T5 disc (top of the thoracic spine); rank sums consistent with the article are 207, 221, and 202. Repeat the test of part (b) for the T4–T5 disc.

Transcribed Image Text:

Subject Position 1 2 3 4 5 Neutral 1.28 0.88 0.69 1.52 0.83 Flexion 1.29 0.76 0.43 2.11 1.07 Extension 1.51 1.12 0.23 1.54 0.20 6 2.58 2.18 1.67