Association and Correlation

Question 1

Scatterplots

Answer 1

Shows the relationship between two quantitative variables measured for the same cases.

Question 2

Positive Association

Answer 2

In general, as one variable increases, so does the other variable. (also called Positive Direction)

Question 3

Negative Association

Answer 3

In general, as one variable decreases, so does the other variable. (also called Negative Direction)

Question 4

Response Variable

Answer 4

Role assigned to the y-axis that you hope to predict or explain.

Question 5

Explanatory Variable

Answer 5

Role assigned to the x-axis that accounts for, explains, predicts, or is otherwise responsible for the y-variable. (also called the Predictor Variable)

Question 6

What Correlation Coefficient measures.

Answer 6

A numerical measure of the direction and strength of a linear association (r).

Question 7

r (formula for correlation coefficient)

Answer 7

Equals the sum of the product of x and y z-scores divided by the count minus one:

r = Σz_xz_y / (n-1) .

Question 8

Monotone Relationship

Answer 8

A relationship that consistently increases or decreases but not necessarily in a linear fashion.

Question 9

Kendall’s tau

Answer 9

Measures the monotonicity directly by recording only whether the slope of a line between two points is positive or negative or zero.

Question 10

Spearman’s rho

Answer 10

Helps find associations even when original data is bent or has outliers by converting x and y variables to ranks and then finding the correlation between the ranks.

Question 11

nonparametric

Answer 11

Measures that are not connected to a specific data model (i.e. not parametric).

Question 12

Lurking Variable

Answer 12

A variable other than x and y that simultaneously affects both variables, accounting for the correlation between the two.

Question 13

Ladder of Powers

Answer 13

^2 - For unimodal distributions skewed to the left or for scatterplots that bend downard.

^1 - Raw data

^1/2 - For counted data.

^”0” - logarithm - For measurements that cannot be negative, especially those that grow by percentage increases.

^-1/2 - unusual but preserves the direction of the relationship

^-1 - For ratios of two quantities

Question 14

When to use squares to re-express data…

Answer 14

Try this for unimodal distributions that are skewed to the left or when a scatterplot bends downward.

Question 15

When to use square root to re-express data…

Answer 15

Count data that needs to be re-express.

Question 16

When to use the negative reciprocal of the square root…

Answer 16

Unusual but sometimes useful to change the sign of data but preserve the direction of relationships.

Question 17

When to use the reciprocal…

Answer 17

Ratios of two quantities (mph, for example) benefit from this. Add a small constant, if data have zeros.