# Correlation Notes

**Topics:**Spearman's rank correlation coefficient, Pearson product-moment correlation coefficient, Covariance and correlation

**Pages:**3 (621 words)

**Published:**November 30, 2013

Chapter 10

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.Scatterplot

•Data are graphed as a scatterplot of pairs of scores.

--HW Q--

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

Pearson

Spearman rank-order

Point-biserial

All between 0 and ±1.0

Calculated differently

Depends on scale of measurement

Pearson Correlation Coefficient

Describes linear relationship

Between two interval or ratio variables

r =

Example...

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