# CORRELATION COEFFICIENT

CORRELATION COEFFICIENT

STATISTICAL TECHNIQUE IN REVIEW

Many studies are conducted to identify relationships between or among variables. The correlational coefficient is the mathematical expression of the relationship studied. Three common analysis techniques are used to examine relationships: Spearman Rank-Order Correlation or rho, Kendall’s Tau or tau, and the Pearson’s Product-Moment Correlation Coefficient or r. Spearman and Kendall’s Tau are used to examine relationships with ordinal level data. Pearson’s Correlation Coefficient is the most common correlational analysis technique used to examine the relationship between two variables measured at the interval or ratio level.

Relationships are discussed in terms of direction and strength. The direction of the relationship is expressed as either positive or negative. A positive or direct relationship exists when one variable increases as does the other variable increases, or when one variable decreases as the other decreases. Conversely, a negative or inverse relationship exists when one variable increases and the other variable decreases. The strength of a relationship is described as weak, moderate, or strong. Pearson’s r is never greater than −1.00 or +1.00, so an r value of −1.00 or +1.00 indicates the strongest possible relationship, either negative or positive, respectively. An r value of 0.00 indicates no relationship. To describe a relationship, the labels weak (r< 0.3), moderate (r = 0.3 to 0.5), and strong (r> 0.5) are used in conjunction with both positive and negative values of r. Thus, the strength of the negative relationships would be weak with r< −0.3, moderate with r = −0.3 to −0.5, and strong with r> −0.5 (Burns & Grove, 2007).

RESEARCH ARTICLE

Source:Keays, S. L., Bullock-Saxton, J. E., Newcombe, P., &Keays, A. C. (2003). The relationship between knee strength and functional stability before and after anterior cruciate ligament reconstruction. Journal of Orthopedic Research, 21 (2), 231–7.

Introduction

Keays et al. (2003) conducted a correlational study to determine “the relationship between muscle strength and functional stability in 31 patients pre- and postoperatively, following a unilateral anterior cruciate ligament rupture” (Keays et al., 2003, p. 231). The results of the study showed a significant positive correlation between quadriceps strength indices and functional stability, both before and after surgery. No significant relationship was demonstrated between hamstring strength indices 60°/s and functional stability, as presented in table 5.

Relevant Study Results

“Patients with an unstable knee as a result of an anterior cruciate ligament (ACL) rupture rely heavily on muscle function around the joint to maintain dynamic stability during functional activity. It is uncertain which muscles play the decisive role in functional stability or exactly which aspect of muscle function is most critical” (Keays et al., 2003, p. 231). “The aim of this study was to assess the relationship between muscle strength and functional stability of 31 patients pre- and postoperatively, following unilateral ACL ligament rupture” (Keays et al., 2003, p. 231). “To assess the relationship between maximum isokinetic strength and functional performance Pearson’s correlations (r) were computed. … Due to the number of correlations computed, and therefore the increased likelihood that chance results may be evident, a more conservative significance level of α = 0.01 was adopted to control for increased Type 1 error” (see table 5; Keays et al., 2003,