EXERCISE23 PEARSON`S PRODUCTMOMENT CORRELATION COEFFICIENT
EXERCISE23 Questions to be Graded
1. Whatis the rvalue for the relationship between Hamstring strength index 60°/sand the Shuttle run test? Is this rvalue significant? Provide a rationale for your answer.
Therelationship between Hamstring strength index 60 degree/s and theShuttle run test is a weak negative relationship due to   r =−0.149 listed in Table 5 since r <0.3 per Pearson’s  Correlation Coefficient.   The r value is not statisticallysignificant since   p = 0.424 > 0.01.
2. Considerr= 1.00 and r= −1.00. Which rvalue is stronger? Provide a rationale for your answer.
Ther values of +1.00 and –1.00 both indicate the strongest possiblerelationships among variables .   Positive (+) 1.00 is thestrongest or perfect positive relationship and indicates thatvariables change together, either increasing or decreasingsimultaneously. Negative (–) 1.00 is the strongest or perfectnegative relationship and indicates that variables change in oppositedirections: as one variable increases another variable decreases.
3. Describethe direction of the relationship between the Hamstring strengthindex 60°/s and the Shuttle run test.
Therelationship between Hamstring strength index 60 degree/s and theShuttle run test is a negative relationship due to r moves away fromzero   in negative direction and   r = −0.149,  the strength of this negative relationships would be weak with r<–0.3.means when Hamstring strength index 60 degree/s  increases and the Shuttle run test   decreases.
4. Withoutusing numbers, describe the relationship between the Hamstringstrength index 120°/s and the Triple hop index.
Therelationship between the Hamstring strength index 120/s and theTriple hop index is r = 0.420 . This is a moderate positiverelationship since the r value falls between 0.3 to 0.5.   The rvalue is also statistically significant since p = 0.019 and this pvalue is less than α = 0.05.
5. Whichvariable has the weakest relationship with the Quadriceps strengthindex 120°/s? Provide a rationale for your answer.
Theweakest relationship between Shuttle run test and Quadriceps strengthindex 120/s with an r = −0.457** and r value is the closest to0.00. So the closer the r value is to zero, the smaller therelationship.
6. Whichof the following sets of variables has the strongest relationship?
a. Hamstringstrength index 120°/s and the Hop index
b. Quadricepsstrength index 60°/s and the Carioca test
c. Quadricepsstrength index 120°/s and the Side step test
d. Quadricepsstrength index 60°/s and the Triple hop index
Theanswer is d
r= 0.431* b. r = −0.474* c. r = −0.519** d. r = 0.619**strongest relationship as its r value is the closest to +1.00.
7.In Table5,two rvalues are reported as r= −0.498 and r= −0.528. Describe each rvalue in words, indicating which would be more statisticallysignificant, and provide a rationale for your answer.
r= −0.498** and p=0.004. The r value listed for the QuadricepsStrength Index 60°/s and Shuttle run test and r=0.498 moderatenegative relationship because r falls between 0.3 to –0. 5.
r=0.528**,and p=0.002. The r value listed for the Quadriceps Strength Index60°/s and side step test and r= 0.528 Strong negative relationshipsince r>0.5
r=0.528**,is more significant since p =0.002< 0.01, where r = −0.498** issignificant at p =0.004< 0.01. The smaller the pvalue in a testof hypothesis the more significant the results are.

The researchers stated that the study showed a positive, significant correlation between Quadriceps strength indices and pre and postoperative functional stability. Considering the data presented in the Table 5, do you agree with their statement? Provide a rationale for your answer.
YesFunctional stability was determined by performance during fivefunctional stability tests that included the shuttle run, side step,carioca, single and triple hop tests. There is a significant positivecorrelation between quadriceps strength indices and all fivefunctional tests postoperatively (p`s < 0.01) and there was asignificant increase in the correlation between quadriceps strengthindices and three functional tests postoperatively (p < 0.05).
9. Theresearchers stated that no significant relationship could bedescribed between Hamstring strength indices 60°/s and functionalstability. Given the data in Table5,explain why not.
Fromthe data given in Table 5, the Hamstring strength indices 60°/s havethe following relationship with the functional stability tests havethe following r values: Hop index (r = 0.247, p = 0.080), Triple hopindex (r = 0.342, p = 0.060), Shuttle run test (r = 0.149, p =0.424), Side step test (r = 0.124, p = 0.506), and Carioca test (r =0.047, p =0.802). It can be seen that all the relationships ofHamstring strength indices 60°/s with the functionality stabilitytests, the probability or p values of the r values are all greaterthan the significance level set at α = 0.01 and α = 0.05.These pvalues do not represent significance at the 5% level.
10. Considerthe relationship reported for the Quadriceps strength index 120°/sand the Hop index (r= 0.744**, p= 0.000). What do these rand pvalues indicate related to statistical significance and clinicalimportance?
Apositive or direct relationship exists between these two variables,indicating that the Quadriceps strength and Triple hop indices eitherincrease or decrease together. This is a strong relationship sincethe r >0.5.The r value is also statistically significant since p=0.000 and this p value < 0.01. The results were statisticallysignificant with a P Value of less than 0.01 and r=0.744 is alsoclinically significant due to strong effect size and large percentageof variance in functional stability. 
References
Grove,Susan K. Statisticsfor Health Care Research: A Practical Workbook.W.B. Saunders Company, 022007. VitalBook file.