Week 9

Question 1

What is correlation?

Answer 1

Statistical technique used to measure and describe the degree to which a pair (or more) of variables are related.

Question 2

What 2 characteristics does the numerical value of correlation measure and describe?

Answer 2

1. The direction of the relationship.

2. The strength and consistency of the relationship.

Question 3

What are the +/- signs used for when describing the direction of the correlational relationship?

Answer 3

To indicate if a relationship is positive or negative.

Question 4

What is a positive correlational relationship?

Answer 4

Two variables change in the same direction (one variable increases, so does the other).

Question 5

What is a negative correlational relationship?

Answer 5

Two variables change in opposite directions (one variable increases, the other decreases).

Question 6

What is a perfect correlation?

Answer 6

Change in one variable is accompanied by a perfectly predictable change in the other variable.

Question 7

What numerical value would be used to describe a perfect correlational relationship?

Answer 7

1.00 (or -1.00 for negative relationships).

Question 8

What numerical value would be used to describe a correlational relationship with no consistency at all.

Answer 8

0.00

Question 9

What is Pearson correlation?

Answer 9

Measures degree and direction of the linear relationship between two variables.

Question 10

What notation is used for Pearson correlation for a sample?

Answer 10

r

Question 11

What notation is used for Pearson correlation for a population?

Answer 11

ρ (rho).

Question 12

How would you express Pearson correlation formula using words?

Answer 12

The covariability of X and Y divided by the variability of X and Y separately.

Question 13

What is the sum of products?

Answer 13

A value used to measure the amount of covariability between two variables.

Question 14

What notation is used to represent the sum of products?

Answer 14

SP.

Question 15

What is the definitional formula for the sum of products (SP)?

Answer 15

SP = Σ(X-Mₓ)(Y-Mᵧ)

Question 16

What is the computational formula for the sum of products (SP)?

Answer 16

SP = ΣXY - (ΣXΣY/n)

Generally easier

Question 17

What is the formula for Pearson correlation (r)?

Answer 17

r = SP/√SSₓSSᵧ

Question 18

What is a scatterplot?

Answer 18

Data display that shows the relationship between two numerical variables (visual representation of SP).

Question 19

What information can a scatterplot detect?

Answer 19

1. Non-linear relationships.
2. Outliers.
3. Sub-groups.

Question 20

What is a non-linear (curved) relationship?

Answer 20

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.

Question 21

What would you expect to see in a scatterplot if sub-groups were present?

Answer 21

Clusters of scores in distinct regions of the graph.

Question 22

Is Pearson correlation appropriate for non-linear relationships?

Answer 22

No.

Question 23

What are the general Pearson correlation strength guidelines?

Answer 23

Extremely weak: Less than 0.10
Weak: 0.10 to 0.29
Moderate: 0.30 to 0.49
Strong: 0.50 or more

Question 24

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?

Answer 24

The shape and correlation would remain the same.

Question 25

If you were to multiply or divide every X or Y score in the dataset by a constant, how would this change shape and correlation?

Answer 25

The shape and correlation would remain the same.

Question 26

How do you express X and Y taken from a scatterplot as z-scores?

Answer 26

Zₓ and Zᵧ.

Question 27

What is the Pearson correlation formula using z-scores for a sample?

Answer 27

r = ΣZₓZᵧ/(n-1)

Question 28

What is the Pearson correlation formula using z-scores for a population?

Answer 28

ρ = ΣZₓZᵧ/N

Question 29

List the applications of correlation? (where and when is it used?).

Answer 29

1. Prediction.
2. Validity.
3. Reliability.
4. Theory verification (kind of prediction…)

Question 30

When interpreting correlations, list the 4 main things you should keep in mind.

Answer 30

1. Correlation does not equal causation.
2. The correlation value can be affected greatly by the range of scores represented in the data.
3. Outliers can have dramatic effects on correlation value.
4. Do not focus on the correlation numerical value.

Question 31

The correlation value can be affected greatly by the range of scores represented in the data, why?

Answer 31

The data collected may not represent the entire range of possible scores, for example a biased sample.

Question 32

Outliers can have dramatic effects on correlation value, how is this possible?

Answer 32

Even one very extreme score can distort a scatterplot to show positive results.

Question 33

Define the coefficient of determination (sometimes called the squared correlation or r²).

Answer 33

The proportion of variability in the data that is explained by the relationship between X and Y.
(For example, 50% of the variability in the Y scores can be predicted from the relationship with X.)

Question 34

What is partial correlation?

Answer 34

The relationship between two variables while controlling the influence of a third variable by holding it constant.

Question 35

What is the null and alternative hypothesis for correlation?

Answer 35

H₀: ρ = 0

H₁: ρ ≠ 0

Question 36

Why is the df for correlation t-tests n-2?

Answer 36

Because if a sample of two was used it would always result in a perfect correlation. (imagine two dots on a scatterplot with a line drawn between them).

Question 37

What is the formula for the standard error of r?

Answer 37

Sᵣ = √1-r²/n-2

Question 38

What is the formula for the correlation t-statistic?

Answer 38

t = r - ρ/Sᵣ