Correlation (Statistical overview)

Authors

Affiliations

Nate Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

Definition

Correlation

“Correlation is a statistical technique that can show whether, and how strongly, pairs of variables are related. There are several different correlation techniques, including the Pearson or product-moment correlation”¹

Monotonic association between 2 variables(Schober et al., 2018)

1. one variable increases → other increases
2. One variable increases → Other Decreases

Variance

Measure of the variability of a single variable²

Covariance vs Variance

Covariance is similar to variance, but whereas variance describes the variability of a single variable²

Covariance

Defined as the Degree to which the change in 1 continuous variable is associated with the change in another continuous variable²

Covariance is a measure of how 2 variables vary together²

Covariance vs Variance

Covariance is similar to variance, but whereas variance describes the variability of a single variable²

Intra-class Coefficient (ICC)

• 0-1 (higher is better)
• Correlations between repeated measurements within a class of data³

Correlation coefficient

Describes Strength & Direction of association between variables

Coefficient of Determination (R^2)

Proportion of variance in 1 variable that is accounted for by the other² .

Linear correlation

See more about linear correlation

Interpretation

See We considered a correlation coefficient of .00–0.30 to be very weak, 0.31–0.50 weak, 0.51–0.70 moderate, 0.71–90 strong and 0.91–1.00 very strong as proposed by Mukaka

Note

Mukaka MM. Statistics corner: A guide to appropriate use of correlation coefficient in medical research. Malawi Med J. 2012;24(3):69–71.

References

1.

Giavarina D. Understanding Bland Altman analysis. Biochemia Medica. 2015;25(2):141-151. doi:10.11613/BM.2015.015

2.

Schober P, Boer C, Schwarte LA. Correlation Coefficients: Appropriate Use and Interpretation. Anesthesia and Analgesia. 2018;126(5):1763-1768. doi:10.1213/ANE.0000000000002864

3.

Liljequist D, Elfving B, Skavberg Roaldsen K. Intraclass correlation - A discussion and demonstration of basic features. PloS One. 2019;14(7):e0219854. doi:10.1371/journal.pone.0219854