Question

Callahan (2009) demonstrated that Tai Chi can significantly reduce symptoms for individuals with arthritis. Participants were 18 years old or older with doctor-diagnosed arthritis. Self-reports of pain and stiffness were measured at the beginning of an 8-week Tai Chi course and again at the end. Supposed that the data produced an average decrease in pain and stiffness of MD=7.5 points with a standard deviation of 20.5 for a sample of n=40 participants
a.) Use a two-tailed test with alpha =.05 to determine whether the tai chi had a significant effect on pain and stiffness.

b.) compute Cohen's D to measure the size of the treatment effect.

Answer 1

a)

mean of difference ,    D̅ =    7.500                  
                          
std dev of difference , Sd =        20.5000                  
                          
std error , SE = Sd / √n =    20.5000   / √   40   =   3.2413      
                          
t-statistic = (D̅ - µd)/SE = (   7.5   -   0   ) /    3.2413   =   2.314
                          
Degree of freedom, DF=   n - 1 =    39                  
t-critical value , t* =    ±   2.0227   [excel function: =t.inv.2t(α,df) ]               
                          
p-value =        0.0260   [excel function: =t.dist.2t(t-stat,df) ]               
Decision:   p-value <α , Reject null hypothesis                      

b)

  
cohen's d = |Dbar/ std dev| =    0.37