What is a correlation?
- Looks ar relationships or associations between variables
- Do changes in x, relate to changes in y? (If so we can then infer)
What is an example of how correlations can relate to clinical measures and instrumentation?
RPE and HR Correlation
* RPE (Ask how they feel)
* HR (Machine to measure)
Strength of Correlations
- The closer to 1 the stronger the relationship (+1 or -1)
- Data is tight to linear line formation
Directions of Relationships
- Direct: As y goes up, x goes up (Heads Northeast)
- Indirect: As y goes down, x goes up (Head Southeast)
- The more horizontal the line the more likely it is 0.
What correlation tests do we do for different measures?
- Interval or Ratio = Pearson Product Moment Correlation Coefficent
- Rank or Mixed (One Rank, One Interval or Ratio) = Spearman rho rank correlation coefficent
Categorical data CANNOT be correlated. (Aka Nominal)
How many people do you want for a correlational study?
At least 30!
After we run the correlation coefficent test, how do we visualize the data?
- Use a scatter plot!
- Put a linear line
- Get r^2 value
On the coefficent test it may have significance as a line, is this important?
No ignore it.
The weaker the relationship the harder it is to ____ interpret.
visually
Coefficent r meaures a ____ relationship only!
linear
Curvilinear relationship will not be described well by a correlation coefficent.
What is a Cubic and Quadratic Relationship?
- Cubic relationship: curve to it (this leads to over and underestimating relationships); See photo attached.
- Quadratic relationship: goes up and goes down. Prabala; Ex: Arousal graph
When we create a scatter plot and get a quadratic curve, what does this mean about the relationship?
- There is no linear relationship
- This does not mean that their is no relationship.
A correlation is not a
proportion
- Correlation is not a proportion (ie. .40 is not 2 x’s as strong as .20 or the difference between .50 and .60 not necessarily the same as between .80 and .90 – variable dependent)
Coefficent of determination (r^2)
- % of the total variance in Y scores that can be explained by the X scores. (Tells you how much variation is explained by the other measures. Tells you the quality of measures.
- If r=.87, r^2=.76; therefore 76% of the variance of Y is explained by X.
- 1-r^2 is the proportion of variance not explained (24%).
We want to have a spread in ____ and ____ for a correlational study.
X and Y
The ____ of a correlation does not mean that the coefficient represents a strong relationship.
significance
____ should not be discussed as being clinically important just because they have achieved significance.
Low correlations
If we have a low correlation, what should we report?
Report the R^2!
Correlation ____ Comparison
- does not equal
- Just means there is a relationship if correlation is high
Correlation and Causation
- X does not cause Y or Y does not cause X
- Correlation: relationship
- Cause and effect is better determines by experimental design
Other considerations for correlations
- Range of Test Values (Generalization should be limited to the range of values used to generate the correlation coefficents
- Restriction in the Range of Scores (Need a full range of X and Y; avoid ceiling and flooring effects!)
- Assumption of Independence (No sense correlating values together that are also use to help calculate on of the two variables compared; Ex: Gait velocity and distance, distance/time = velocity, therefore will obviously have a connection.
What are partial correlations?
- A technique that allows one to describe the relationship of more than one variable.
Example:
- How well does PT Board exam scores related to undergraduate GPA (UG GPA) and PT coursework GPA (PT GPA)?
- Some overlap of UG GPA with PT Board but also PT GPA and PT Board; in addition UG and PT GPA have some overlap
Y =
- What I am trying to understand
- Ex: HR
X =
- What I am manipulating
- Ex: Dosage
