Association Claims and Correlations
Association Claims
Deals with two variables and how they relate to each other.
Statements about the correlation between two variables.
Correlation: How two variables relate to each other; as one variable changes, what happens to the other one.
Examples of Association Claims
Shy people are better at reading facial expressions:
Variables: Shyness and skill at reading facial expressions.
Claim: Higher shyness is associated with better facial expression reading.
The more narcissistic you are, the less you think of others:
Variables: Level of narcissism and opinion of others.
Claim: Higher narcissism is associated with a lower opinion of others.
Children who go to better preschools get into better colleges:
Variables: Quality of preschool and quality of college.
Claim: Higher preschool quality is associated with higher college quality.
Correlation Types
Association claims imply a correlation between variables.
Positive Correlation
As one variable increases, the other variable increases, and as one decreases, the other decreases.
Negative Correlation
As one variable increases, the other decreases. Variables move in opposite directions.
Examples Revisited
Shy people are better at reading facial expressions:
Positive correlation: As shyness increases, the ability to read facial expressions increases.
The more narcissistic you are, the less you think of others:
Negative correlation: As narcissism increases, the opinion of others decreases.
Children who go to better preschools get into better colleges:
Positive correlation: As the quality of preschool increases, the quality of college increases.
Association Claims vs. Frequency Claims
Association claims deal with two variables, whereas frequency claims deal with only one.
In association claims, both variables are measured, not manipulated.
Measuring Variables
To establish a potential correlation between hours of TV watched and childhood obesity, one would measure these two variables and then assess their relationship. A frequency claim would only consider one variable, such as the percentage of children who are obese.
Scatter Plots
Ideal for visualizing the direction and strength of correlations.
Each dot represents an observation of one person's values on two different variables.
Shows the relationship between two variables measured on a group of people.
Trend Lines (Lines of Best Fit)
Show the direction of the relationship.
Drawn to be as close as possible to all points, representing the overall trend.
Positive Correlation in Scatter Plot
Trend line points up and to the right.
Higher values on one variable are associated with higher values on the other variable.
Negative Correlation in Scatter Plot
Trend line points from upper left to lower right.
As one variable increases, the other decreases.
The slope of the line indicates direction; negative slope means negative correlation.
Zero Correlation in Scatter Plot
Points appear cloud-like with no clear direction.
Trend line is horizontal, indicating no relationship between the two variables.
Interpreting Scatter Plots
Individual points: Represent individual data points, and show deviation from potential models.
Horizontal trend line: Lack of relationship between two variables. As one variable changes, it doesn't impact the other one.