The WeaverDunn procedure with a fiber mesh tape augmentation

The Weaver-Dunn procedure with a fiber mesh tape augmentation is commonly used to treat AC joint (a joint in the shoulder) separations requiring surgery. The article ``TightRope Versus Fiber Mesh Tape Augmentation of Acromioclavicular Joint Reconstruction\'\' (Am. J. Sport Med., 2010: 1204-1208) described the investigation of a new method which was hypothesized to provide superior stability (less movement) compared to the W-D procedure. The authors of the cited article kindly provided the accompanying data on anteposterior (forward-backward) movement (mm) for six matched pairs of shoulders:

Carry out a test of hypotheses at significance level 0.01 to see if true average movement for the TightRope treatment is indeed less than that for the Fiber Mesh treatment. Be sure to check any assumptions underlying your analysis.

Solution

Set Up Hypothesis
Null, Ho: u1 = u2
Alternate, TightRope treatment is indeed less than that for the Fiber Mesh - H1: u1 > u2
Test Statistic
X(Mean)=28.333
Standard Deviation(s.d1)=6.653 ; Number(n1)=6
Y(Mean)=15
Standard Deviation(s.d2)=3.464; Number(n2)=6
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =28.333-15/Sqrt((44.26241/6)+(11.9993/6))
to =4.35
| to | =4.35
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 5 d.f is 3.365
We got |to| = 4.35409 & | t | = 3.365
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 4.3541 ) = 0.00367
Hence Value of P0.01 > 0.00367,Here we Reject Ho

We have evidence to indicate that true average movement for the TightRope treatment
is indeed less than that for the Fiber Mesh treatment