L06 Correlations

Question 1

Correlations - what?

Answer 1

Associations between variables

How closely the data points fall to the line of best fit

Question 2

4 measures of association

Answer 2

1. Covariance
2. Correlation:
   - Pearson’s coefficient of correlation
   - Variance accounted for (or explained)
3. Spearman’s coefficient of rank correlation

Question 3

Covariance - formula

Answer 3

Mean of the Product of Deviations
Cov(X,Y) = sum of (xi-xbar)*(yi-ybar) / n

Unit: of x*y

Question 4

Covariance - features

Answer 4

• Crude measure of correlation measured for calculating Pearson’s r
• Parametric test
• Unit depends on x and y: not standardized
• +/- higher value means stronger correlation

Question 5

2 key tests of correlation

Answer 5

1. Pearson’s coefficient of correlation

2. Spearman’s Rho Correlation Coefficient

Question 6

Pearson’s Coefficient of Correlation - when?

Answer 6

Linear relationship

2 continuous variables

Question 7

Spearman’s Rho Correlation Coefficient - when?

Answer 7

Correlation between ranked or ordinal data
Non-parametric; so no assumption of normality
No assumption of even spacing

Question 8

Line of Best Fit

Answer 8

Added in a scatterplot
Line that best represents data
Correlation: how closely data points fall to this line
Regression: the characteristics or equation of the line
A good line of best fit - very small residuals for each point

Question 9

Correlation of magnitude 1? 0?

Answer 9

1- Perfect (+/-) relationship

0 - no linear relationship

Question 10

Pearson’s correlation coefficient symbol

Answer 10

r

Question 11

Pearson’s correlation coefficient formula

Answer 11

r= Cov(X,Y) / sx sy
where Cov(X,Y) = Covariance of X and Y
 sx and sy = standard deviations of the variables

Unit: no unit; standardized
Independent of overall variability

Question 12

Pearson’s correlation coefficient features

Answer 12

Linear relationship between 2 continuous variables
r = covariance of the two divided by SDs
No unit; standardized
Because divided by SD, independent of overall variability (so it only shows how well-related the variables are and not how much they vary)

Question 13

what is R squared

Answer 13

Variance accounted for

Question 14

Variance accounted for

Answer 14

Amount of variance explained by the data
Expressed as % or a fraction
Rsquared - square of Pearson’s r

Question 15

What does Rsquare close to 1 mean?

Answer 15

Variance accounted for near 1 -> almost all the variation in data is shared between variables/explained by data

Question 16

Partial correlation

Answer 16

“Quantifies the relationship between two variables while accounting for the effects of a THIRD variable on BOTH variables in the original correlation”

The part of correlation that is not related to variable C

Question 17

Semi-partial correlation

Answer 17

“Quantifies the relationship between two variables while accounting for the effects of a third variable on only ONE of the variables in the original correlation”

Question 18

Variable C in a partial correlation is called

Answer 18

Variable that is partialized out or held constant

Question 19

Zero order correlation

Answer 19

Another term for a simple bivariate correlation

as opposed to partial correlations

Question 20

First or second order correlation

Answer 20

Partial correlation that partials out one/two variables

Question 21

Is significance of correlation equal to importance?

Answer 21

Correlation can be significant but weak.

Strength and significance of correlation are not linked,

Question 22

Why do we use correlations?

Answer 22

1. May highlight possible causal relations (though doesn’t imply it)’
2. Null effects / absence of correlations allow us to discount some theories
3. presence: correlation -> investigate why: experiment

Question 23

Biserial correlation

Answer 23

For when a dichotomy has an underlying continuum
One variable is categorical, other continuous
r is called a “point-biserial r”

Question 24

Small, medium and large correlation values

Answer 24

+/- 0.1 small effect
+/- 0.3 medium effect
+/- 0.5 large effect

Question 25

Correlations assumptions

Answer 25

1. Continuous level of measurement: ratio/interval
2. Linear relationship between variables
3. No outliers
4. For small sample, normal population