# Pearson’s Product – Moment Correlation Coefficient Essay Sample

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The r value for the relationship between Hamstring strength index 60o and the Shuttle run test is -0.149. This r value shows a weak correlation between the two variables, as it is less than the 0.3 threshold for significance. Therefore, the r value is not significant. Question 2

Between r=1.00 and r=-1.00, there is no difference in terms of strength. Both values are on the extreme ends of the spectrum and signify the maximum significance within the r value scale. A value of 1.00, whether negative or positive, shows that the two variables have a perfect linear relationship, and as such, the independent variable can be used to accurately predict the value of the dependent variable. The only difference is that the negative value signifies that a rise in one variable causes the corresponding variable to drop while the positive value signifies that the rise in one variable causes the corresponding variable to increase in value as well. But strength wise, they are similar. Question 3

The relationship between the hamstring strength index 60o and shuttle run test index is a negative one. This is signified by the negative nature of the r value (-0.498). A negative relationship occurs when a rise in one variable causes the corresponding variable to decrease in value. Question 4

This research study had the primary objective of measuring the relationship between muscle strength and functional ability. The muscle strength this particular question is concerned with is represented by the hamstring strength index 120 o while the functional ability is represented by the triple hop strength. The positive nature of the relationship, means that the stronger the hamstring muscle, which is signified by a high value in the muscle strength index, the higher the functionality, which is represented by a high score in the triple hop test. Conversely, the lower the muscle strength, the lower the score a respondent will register in the functionality test. Question 5

The shuttle run test has the weakest relationship with the quadriceps strength index 120 o. This is because, it has the r value closest to zero, and zero is the point which signifies no relationship between two variables. The farther the r value is from zero, whether the number is positive or negative; the stronger the relationship. Question 6

The values for the relationships given are:
a. Hamstring strength index 120 o and the hop index: 0.431
b. Quadriceps strength index 60 o and the Carioca test: -0.474 c. Quadriceps strength index 120 o and the Side step test: -0.519 d. Quadriceps strength index 60 o and the triple hop test: 0.619 As already established, the strongest relationship between multiple r values will be the relationship with an r value farthest from zero. This will be option d, the Quadriceps strength index 60 o and the triple hop test. Question 7

The first r value would be negative four hundred and ninety eight thousandths while the second one will be negative five hundred and twenty eight thousandths when both are converted to word form. The second value, negative five hundred and twenty eight thousandths, will be more statistically significant as it is farther from zero, signifying a stronger linear relationship. Question 8

The data provided has two quadriceps strength indices, the 60 o and the 120o indices. However, table 5 only has the post-operative relationship data, therefore, it is impossible to agree or disagree with the researchers’ claims as concerns the pre-operative relationships. Working with the post-operative data provided, it is already clear that there are multiple negative r values in both quadriceps strength indices, specifically in their relationship with the shuttle run test, side step test as well as the carioca test. While all r values are significant (more than 0.3 away from zero both negatively and positively), the statement is wrong in stating that all the relationships between the quadriceps strength indices and functionality were positive. Question 9

As concerns the hamstring strength index 60o and the multiple tests of functional stability, the researchers’ claims can be seen as valid since in 4 of the 5 tests of stability, the r values within a distance of less than 0.3 from zero. The only exception is the triple hop step whose r value is 0.342, which is still a weak relationship. Therefore, the researchers’ claims are valid as per the data provided. Question 10

The r value for the relationship between the quadriceps strength index 120o and the hop index is 0.744 which shows a very strong, and positive, relationship between the two variables. The p value measures the significance of the relationship by showing the probability that the main hypothesis being tested is wrong (and as such, the null hypothesis should be adopted). Since the hypotheses being tested are not outlined, it is to be assumed that the hypothesis was that there will be a relationship between the muscle strength and functional stability; this would make the null hypothesis become ‘there is NO relationship between muscle strength and functional stability’. Since the p value for the quadriceps strength index 120o has a set threshold of 0.01 (as per the postscript in table 5), then any value higher than 0.01 renders the relationship statistically insignificant (and the null hypothesis is accepted). Clinically, this would make the results unreliable. The p value however is 0.000 which makes the results accurate and useful for future related studies.