Linear Correlation

Authors
Affiliations

Doctor of Physical Therapy

B.S. in Kinesiology

Doctor of Physical Therapy

B.A. in Neuroscience

Linear regression vs Pearson product vs Spearman rank coefficient

Comparison of differing “r” and “\rho” values (From figure 3 of Schober et al. 20181)

Comparison of differing “r” and “ρ” values (From figure 3 of Schober et al. 2018)

Linear Regression

Usually when the independent variable is fully controlled

  • 1 independent variable (x)
  • 1 dependent variable (y)

Purpose: estimation of y-values from x-values

Pearson Product Moment Correlation (r)

Read more about Pearson Product Moment Correlation (r)

Generally applied when both variables are observed

  • 2 continuous random variables

  • Purpose: Correlation Coefficient

    • Measure strength of the relationship
    • Conventionally applied when both

Spearman Rank Coefficient (ρ)

Read more about Spearman Rank Coefficient (ρ)

  • 2 Continuous random variables
  • 1 variable is ordinal and ranked
    • Converts non-linear to ranked-linear

Purpose: Correlation Coefficient

References

1.
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

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