Notes on Correlation in Strength and Conditioning

Correlation in Strength and Conditioning

Correlation is a statistical method used to describe or quantify the relationship between two independent variables.
It provides an estimation of the strength and direction of the relationship.
Example: The scatter plot demonstrating the relationship between concentric impulse and jump height showcases a strong relationship due to the mechanical link; correlation can quantify this.

Assumptions for Correlation

Data for both variables should be normally distributed (bell curve).
The relationship between the variables should be linear.
There should be no outliers in the data set.
Observations should be independent (no multiple observations from the same participant).
Violating the independence assumption overestimates the magnitude of the relationship.

Types of Correlation Coefficients

Pearson correlation coefficient: The most common method.
Spearman rank correlation: Ranks the data and assesses the similarity between the ranks of the two variables.

Interpreting Correlation

Avoid the binary interpretation of only considering statistical significance (p < 0.05).
P-value indicates whether the relationship is more extreme than expected in the normal population, not the strength.
Interpret the strength of the relationship qualitatively within the context of the data.

Qualitative Scale

Correlations range from -1 to 1.
- Negative correlation: less than zero.
- Positive correlation: more than zero.
- Zero: no relationship.
Describe the strength of the relationship based on the numerical value.

Examples

Correlation close to 1: strong relationship (as one variable increases, so does the other).
Correlation close to 0: weak to negligible relationship (changes in one variable do not affect the other).

Coefficient of Determination

Describes the proportion of variability in one measure explained by the other.
Calculated by squaring the correlation coefficient ( $r^2$ ).
Example: If $r = 0.099$ , then $r^2$ explains the variance jump height explained by concentric impulse.

Interpreting Coefficient of Determination

Example: Concentric impulse increases, so does jump height.
High $r^2$ means almost perfect causal relationship for jump height, supported by physics.

Causation vs. Correlation

Correlational analysis does not imply causation. Just describes the statistical relationship.
Correlation is a descriptive statistic.

Impact of Sample Size

Small sample size may not represent the population, limiting the relevance of the correlation.
Larger sample sizes increase the likelihood of finding a statistically significant relationship (lower p-value).

Linearity Assumption

Pearson's R assumes a linear relationship, which may need to be valid
Example: Strength loss and functional capacity have a non-linear relationship, so correlation has to be careful.

Considerations

Always consider the basis for the relationship between variables, not just the statistical output.
Be cautious when interpreting correlations; think if the relation is linear or not.