Week 9 Flashcards
What is correlation?
Statistical technique used to measure and describe the degree to which a pair (or more) of variables are related.
What 2 characteristics does the numerical value of correlation measure and describe?
- The direction of the relationship.
2. The strength and consistency of the relationship.
What are the +/- signs used for when describing the direction of the correlational relationship?
To indicate if a relationship is positive or negative.
What is a positive correlational relationship?
Two variables change in the same direction (one variable increases, so does the other).
What is a negative correlational relationship?
Two variables change in opposite directions (one variable increases, the other decreases).
What is a perfect correlation?
Change in one variable is accompanied by a perfectly predictable change in the other variable.
What numerical value would be used to describe a perfect correlational relationship?
1.00 (or -1.00 for negative relationships).
What numerical value would be used to describe a correlational relationship with no consistency at all.
0.00
What is Pearson correlation?
Measures degree and direction of the linear relationship between two variables.
What notation is used for Pearson correlation for a sample?
r
What notation is used for Pearson correlation for a population?
ρ (rho).
How would you express Pearson correlation formula using words?
The covariability of X and Y divided by the variability of X and Y separately.
What is the sum of products?
A value used to measure the amount of covariability between two variables.
What notation is used to represent the sum of products?
SP.
What is the definitional formula for the sum of products (SP)?
SP = Σ(X-Mₓ)(Y-Mᵧ)
What is the computational formula for the sum of products (SP)?
SP = ΣXY - (ΣXΣY/n)
Generally easier
What is the formula for Pearson correlation (r)?
r = SP/√SSₓSSᵧ
What is a scatterplot?
Data display that shows the relationship between two numerical variables (visual representation of SP).
What information can a scatterplot detect?
- Non-linear relationships.
- Outliers.
- Sub-groups.
What is a non-linear (curved) relationship?
A relationship between two variables in which change in one variable does not correspond with constant change in the other variable but a pattern is still present.
What would you expect to see in a scatterplot if sub-groups were present?
Clusters of scores in distinct regions of the graph.
Is Pearson correlation appropriate for non-linear relationships?
No.
What are the general Pearson correlation strength guidelines?
Extremely weak: Less than 0.10
Weak: 0.10 to 0.29
Moderate: 0.30 to 0.49
Strong: 0.50 or more
If you were to add or subtract a constant to/from every X or Y score in the dataset, how would this change shape and correlation?
The shape and correlation would remain the same.