Correlation

Question 1

What is the Pearson product-moment correlation coefficient?

What symbol is it represented by?

Answer 1

It looks at whether variables deviate from the mean in a similar way (co-vary)
BUT it is on a standardized scale to facilitate comparisons across units of measurement

denoted by “r”

Question 2

What type of data can the Pearson correlation coefficient (or its adaptations) be used for?

Answer 2

Typically associated with looking at the relationship between variables measured on an interval or ratio scale
HOWEVER it can also be used for:
1. Ordinal variables when the raw scores have been converted to ranks
2. An interval or ratio scale variable with a dichotomous variable
3. Two dichotomous variables
Note that these have become adaptations with difference names

Question 3

List all types of variable combinations that adaptations of Pearson correlation coefficients can be used for

Answer 3

1. Interval/Ratio + Interval/Ratio
2. Ordinal (ranked) + Ordinal (ranked)
3. Nominal (dichotomous) + Nominal (dichotomous)
4. Nominal (dichotomous) + Interval/Ratio

Question 4

What are the names of the simplified Pearson correlation coefficient formulas?

Answer 4

1. Phi
2. Spearman
3. Point-biserial correlation
4. Pearson correlation

Question 5

What type of data is the Phi correlation coefficient used for?

Answer 5

Nominal (dichotomous) + Nominal (dichotomous)

Question 6

What type of data is the Point-biserial correlation coefficient used for?

Answer 6

Nominal (dichotomous) + Interval/Ratio

Question 7

What type of data is the Spearman correlation coefficient used for?

Answer 7

Ordinal (ranked) + Ordinal (ranked)

Question 8

What type of data is the Pearson correlation coefficient used for?

Answer 8

Interval/Ratio + Interval/Ratio

Question 9

What is the Spearman correlation coefficient denoted by?

Answer 9

p or r subscript s

Question 10

When ranking data for a spearmen correlation coefficient - what do you do if two have the same value?

Answer 10

You give both scores the same averaged rank
e.g. if those values would be rank 5 and 6 (but are the same so it wouldn’t be possible order them) you would take the average of 5 and 6 (5.5) and assign both of the values the rank of 5.5

Question 11

How do you interpret a correlation coefficient?

Answer 11

The correlation coefficient has to lie between -1 and +1

A coefficient of +1 indicates a perfect positive relationship, a coefficient of -1 indicates a perfect negative relationship, a coefficient of 0 indicates no linear relationship at all

Question 12

When used as a measure of effect size, what would small medium and large effect size of a correlation coefficient be?

Answer 12

The correlation coefficient is a commonly used measure of the size of an effect: values of ±.1 represent a small effect, ±.3 is a medium effect and ±.5 is a large effect

Question 13

What type of correlation coefficient can be used for non-parametric data?

Answer 13

Spearman
Kendall’s tau

Both used for ranked ordinal data

Question 14

When should Kendall’s tau be used instead of Spearman?

Answer 14

When you have a small data set and many of the scores in your dataset have the same rank

Question 15

What does the Kendall’s tau correlation coefficient compare?

Answer 15

It looks at the number of concordant and discordant pairs

Question 16

What does the biserial correlation coefficient do?

Answer 16

Estimates the degree of association between dichotomized continuous measure and a continuous measure

Question 17

What is the difference between the biserial correlation coefficient and the point-biserial correlation coefficient?

Give 2 examples

Answer 17

Biserial is used if the dichotomous variable has an underlying continuum between categories

e. g., of a dichotomous variable with underlying continuum passing or failing an exam -> some people might fail by a little bit vs a lot
e. g. of a dichotomous variable without an underlying continuum is being alive or dead (can’t be a bit dead)

Question 18

How does the interpretation of the biserial correlation coefficient differ from that of the point-biserial correlation coefficient

Answer 18

Interpretation of biserial is slightly different because it is an estimate of of the degree of association of the artificially dichotomized continuous variable if it had been evaluated as a true continuous variable

Question 19

What is the rank biserial correlation coefficient used for?

what is a caution for interpretation

Answer 19

To estimate the degree of association between a dichotomized continuous variable with an ordinal (ranked) variable

same caution as biserial -> estimate of the association had the artificially dichotomized variable been examined as continuous

Question 20

What is the phi-biserial correlation used for?

Answer 20

used to examine the association between a true dichotomous variable and a continuous variable that has been dichotomized

Question 21

What is the tetrachoric correlation used for?

Answer 21

to examine the association between 2 artificially dichotomized continuous variables

Question 22

What are 2 other types of correlation coefficients that are often seen in structural equation modeling?

Answer 22

Polyserial correlation

Polychoric correlation

Question 23

What is the Polyserial correlation used for

Answer 23

interval-scaled variable and continuous variable that has been dichotomized or categorized (ordinal)

Question 24

What is the Polychoric correlation used for?

Answer 24

two continuous variables that have been dichotomized or categorized