Covariance and Correlation
What does it mean to say that two variables are associated with one another? How can we mathematically formalize the concept of association?
Differences between Data Handling in Correlation & Experiment 1.
Summarize entire relationship
We don’t compute a mean Y (e.g., aggressive behavior) score at each X (e.g., violent tv watching). We summarize the entire relationship formed by all pairs of X-Y scores. This is the major advantage of correlation. 2.
N = number of pairs
Because we look at all X-Y pairs at once, we have ONE sample, with N representing the number of pairs 3.
Variable X and Variable Y are arbitrary
Either variable can be X or Y. It’s arbitrary. There is no IV or DV. 4.
Data are graphed as a scatterplot of pairs of scores.
The statistic that we calculate to determine the relationship between our variables is the Correlation Coefficient
This number tells us two things about the relationship:
Type of relationship
Strength of relationship
Types of Relationships
Linear: as scores on one variable increase, scores on the other variable either increase or decrease
Nonlinear: relationship between X and Y changes direction at some point
U: Age & difficulty moving
Inverted U: Alcohol consumed & feeling well
Correlational research focuses almost entirely on linear relationships
Strength of Relationship
Strength: How far from zero (absolute value)
Direction: Positive or negative
More on Strength
Greater variability in Y scores at each X score means a lower correlation coefficient, and, hence, a weaker relationship. --HW Qs--
3 Correlation Coefficients
All between 0 and ±1.0
Depends on scale of measurement
Pearson Correlation Coefficient
Describes linear relationship
Between two interval or ratio variables
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