Correlation
A statistical procedure that is used to measure and desribe a realtionship between two variables
OR
Two continuous variables that are associated with or related to each other.
INTERVAL OR RATIO SCALES
Uses of Correlation
- Identify relationships between variables
- Predicting Relationships
- Validity and Reliability
Visually determine correlations between two variables
Through a scatterplot or a visual representation of the relationship between the two continuous variables
Three Characterisitics of Correlations
- Direction of the relationship
- Form of the relationship
- Degree of the relationship
Direction of the relationship
Either increasing or decreasing
1. Positive Correlation: as the value of one variable increases the value of the other variable increases (+ sign)
2. Negative Correlation: as the value of one variable increases the value of the other variable decreases (- sign)
Form of the relationship
Either linear or curvilinear
1. If all the data points lie on a straight line then the relationship is linear
2. If the data points lie in a curve line then it is a curved linear
Degree of the relationship
This can tell us if there is a perfect POSITIVE (+1) or a lack of a relationship NEGATIVE (-1)
Variance
Deviation from the mean of a single variable
Covariance
Measure the relationship between two variables.
Helps us determine how much or to what extent the variables change together.
Population and Sample Covariance Formula
See notes
Problem with Covariance
Highly dependent on units of measurement therfore it is unwise to use it as our correlation coefficient value
To fix:
1. standardize covariance by dividing the standard deviation of each of the two variables
2. becoming the correlation of coeficient which is unaffected by the units of measurement
Sample and Population Correlation Coefficient Formulas
See notes
Correlation does not equal casaution
- Cannot prove a cause-and-effect relationship because there is no systematic manipulation of a variable
- Third-variable problem: causality between two variables cannot be assumed because there may be measured or unmeasured variables affecting the results.
- Direction of casuality: Correlation coefficients say nothing about which variable causes the other to change.
Ceiling Effect
An undersirable measurement outcome occurring when the dependent measure puts an artificially “low ceiling” or how high a participant may score.
Floor Effect
The dependent measure artificially retricts how low scores can be
Restriction of Range
We might only look at a subsection of the data and not get the full story or understanding of the relationship between the two variables.
Affected by Measurement Errors or Outliers
- The more error there is in a measure, the smaller the correlation can be
- Can be affected by outliers, one or more extreme data points can greatly affect the value of the correlation. Therefore it can force us to over underestimate the true relationship between the two variables.
Correlation does not equal proportion of variance explained
A correlation of 1.00 does not mean that there is 100% perfectly predictable relation between X and Y. You must square the correlation ———> leading to Coefficient of Determination.
Coefficient of Determination
Measures the proportion of variability in one variable that can be determined from the relationship with the other variable. “Effect Size” for the correlation AKA “Variance Explained”
Correlation = 0.30
Coefficient of Determination = 0.09
