Unit 12: Correlation

Question 1

explain the difference between t and z test

Answer 1

Question 2

• 1-sample t-test

Answer 2

Have the value
you’re testing
against (population
mean) but NO
population SD

Question 3

z-test

Answer 3

have population
mean & SD

Question 4

Correlations are between what kinds of variables

Answer 4

• between two continuous variables
• between a dichotomous variable and continuous one
• between an ordinal variable and a continuous one

not looking at group differences, but looking at the associations between variables.
* If two variables are correlated it means that they co-vary.
* Does not imply causation

Question 5

response variable

Answer 5

dependent

Question 6

explanatory variable

Answer 6

independent

Question 7

A researcher would like to know if a mother’s height
can explain how tall her child will be. Which is the
response variable?

a. child’s height
b. mother’s height
c. father’s height

Answer 7

a. child’s height

Question 8

what do we use correlations for

Answer 8

Two variables that correlate means that as one variable changes, so
does the other. They co-vary.

• A statistically significant correlation indicates that a relation is present
• Null hypothesis: there is no correlation between the variables (or the correlation between the variables is 0)
• Correlations are very flexible
• When two variables are correlated…
• The correlation coefficient quantifies what is common between variables.

Question 9

The Scatter Plot

Answer 9

Shows the relationship between two quantitative
variables measured on the same individuals.

• The values of one variable appear on the horizontal axis,
  and the values of the other variable appear on the vertical
  axis.
• Each individual corresponds to one point on the graph.

The scatter plot is a visual representation of data, plotting two data distributions in one figure (i.e., two values or scores for each individual)

Question 10

what does a scatter plot line mean

Answer 10

• The amount of scatter in the points that are plotted suggests the strength of
  the relationship between variables.
• A positive relationship emerges when the data scatters from the lower left to
  the upper right.
• A negative relationship emerges when the data scatters from the upper left to
  the lower right

Question 11

After plotting two variables on a scatterplot, we describe the relationship by
examining the form, direction, and strength of the association. We look for an
overall pattern …

Answer 11

• Form: linear, curved, clusters, no pattern
• Direction: positive, negative, no direction
• Strength: how closely the points fit the “form” or how scatter versus close

Question 12

Answer 12

negative

Question 13

Answer 13

zero

Question 14

how do we interpret scatterplots? explain negative and positive association

Answer 14

Question 15

Correlation Values

Answer 15

• Correlations range from -1.0 to +1.0.
• Values closer to +/- 1 are considered perfect correlations.
• A positive correlation is indicated by a positive value
• A negative correlation is indicated by a negative value
• The correlation coefficient is a measure of the direction and
  strength of a linear relationship.

Question 16

How do you get the correlation coefficient?

Answer 16

Question 17

The Strength of a Correlation

Answer 17

The sign of the relationship between two variables has nothing to do
with its strength.
* Rule of thumb to determine the strength of a correlation (Visual
Statistics, 2009):
* 0 to .3 are considered “weak” correlations
* .3 to .7 are considered “moderate” correlations
* .7 and above are considered “high” correlation

Question 18

Correlation: properties of r

Answer 18

1. -1 ≤ r ≤ 1
2. The sign indicates the direction of association
3. positive association: r > 0
4. negative association: r < 0
5. no linear association: r  0
6. The closer r is to ±1, the stronger the linear association
7. r has no units and does not depend on the units of
   measurement
8. The correlation between X and Y is the same as the
   correlation between Y and X

Question 19

The Coefficient of Determination

Answer 19

• The proportion of either variable explained by the other variable.
• This value is the significant Pearson correlation value squared: r2xy
• For r=.7; r2 = .49
• 49% of variation in x explained by y OR
• 49% of variation in y explained by x

Question 20

why is correlation useful

Answer 20

Establishing reliability and validity
* Test-retest reliability
* If you just run a t-test between the two occasions, you may end up finding a statistical
difference even on a reliable exam. There is something called “testing effect” where
people may end up doing better the second time they do it.
* However, even if they do end up doing better the second time around, if the exam is
reliable, the two occasions should have strong correlation.
* How different constructs are related to each other

Question 21

The Pearson Correlation

Answer 21

The most commonly-used correlation value is the Pearson Correlation
(formally the Pearson Product Moment Correlation), with the following characteristics (think assumption checks):
* The correlation is bivariate—there are just two variables involved.
* Both variables are measured on at least an interval scale (i.e., continuous data).
* The variables have a linear relationship.
* No significant outliers.
* The sampling distribution to which the data belong is normally distributed.
* (Usually satisfied when your sample size is large)

Question 22

Bivariate correlations

Answer 22

refer to the relationship between two variables.
* There can be correlations between:
* nominal variables (think dichotomous variables),
* ordinal variables,
* interval/ratio variables,
* and variables of different data scales.

Question 23

The Point-Biserial Correlation

Answer 23

• The point-biserial correlation- relationship between dichotomous
  variable and continuous variable
• Dichotomous variable must be coded 0 and 1
• Additional assumption:
• Equal variances in Y for each of the categories of the dichotomous variable
• Calculated the same way

Question 24

Answer 24

Question 25

Answer 25

Question 26

What happens when you fail the assumption checks?

Answer 26

* Spearman Rho and Kendall’s tau * No need to be “normal” * Ordinal scale is okay! * Not too many ties * Kendall’s tau-b corrects for ties * Puts them into rank order and looks for monotonic relations * Positive: Lower on variable A is associated with lower on variable B * Negative: lower on 1 variable is associated with higher on another variable

Question 27

Spearman Rho

Answer 27

It assesses how well the relationship between two variables can be described using a monotonic function

Question 28

Kendall’s tau

Answer 28

Kendall's Tau is a non-parametric measure of relationships between columns of ranked data. The Tau correlation coefficient returns a value of 0 to 1, where: 0 is no relationship, 1 is a perfect relationship

Question 29

monotonic function

Answer 29

A monotonic function is a function which is either entirely nonincreasing or nondecreasing