W6 - Correlation Analysis

Question 1

What does a bivariate scatter plot show?

Answer 1

Relationship between 2 variables that have been measured on 1 sample of subjects.

Question 2

What are the 3 main types of relationships that can be determined from scatter plots, especially when using a line of best fit.

Answer 2

High-high low-low / +ive correlation

High-low low-high / -ive correlation

Little systematic tendency / 0 or NO correlation

Question 3

What does it mean when (on a scatter plot) the points cluster around the line of best fit?

Answer 3

Stronger relationship between the 2 variables

Question 4

What is a correlation coefficient?

Answer 4

Numerical value indicating the extent to which 2 variables are related.

A numerical summary of a bivariate relationship.

Question 5

How is the strength of the relationship between the 2 variables indicated by using correlation coefficient?

Answer 5

Closer the relationship gets to 1 or -1 = stronger the relationship.

So further away from 0 = stronger the relationship

Question 6

On a correlation coefficient line, where is High-low low-high / -ive correlation found?

Answer 6

-1

Question 7

On a correlation coefficient line, where is High-high low-low / +ive correlation found?

Answer 7

1

Question 8

What must be included in a hypothesis?

Answer 8

Effect of interest (difference/relationship)

Variables

Population of interest

Question 9

What is a way of saying we have homogeneity of variance?

Answer 9

Saying the data is HOMOSCEDASTIC

Question 10

What is a way of saying we don’t have homogeneity of variance?

Answer 10

Saying the data is HETEROSCEDASTIC

Question 11

How can you work out how much of the variance in final body temp (i.e) is explained by the running speed (i.e)?

Answer 11

Variance explained = coefficient of determination (R^2)

Then expresses as a decimal or %

Question 12

Does correlation mean causation?

Answer 12

Not necessarily

Question 13

Does correlation mean agreement?

Answer 13

Not necessarily

Question 14

The correlation coefficient between two variables is r = .90. How much common variance do they share? i.e What is the coefficient of determination?

Answer 14

81%

Question 15

What is the correlation coefficient also known as?

Answer 15

r value

Question 16

What is the common variance or variance shared between 2 variables if the relationship between them is represented by a correlation coefficient of 0.8?

Answer 16

r^2 = 0.64

Question 17

What is the % of UNaccounted variance (variance not shared) between 2 variables if the relationship between them is represented by a correlation coefficient of 0.35?

Answer 17

r = 0.35

r^2 = 0.1225

Variance shared = 12.25%

== Variance NOT shared = 87.75%

Question 18

If there’s a strong correlation between the values given by 2 variables, what are the 2 things we can’t say for certain when interpreting that relationship?

Answer 18

CAN’T know for certain that the relationship is CAUSAL.

OR

that (in the case of 2 measures of the same thing) the measures agree w/ each other.

Question 19

Which assumptions can be examined using a only scatterplot graph?

Answer 19

Linearity

Homogeneity of variance

Question 20

How can you find what the common variance between variables is?

Answer 20

Find r^2 value

Square root = r value

r value (i.e 0.444 or 44.4%) = variance shared

Question 21

What are the assumptions of the Pearsons Correlation?

Answer 21

Normality

Linearity

Homogeneity of variance

No obvious outliers

Question 22

Using knowledge of Pearsons Correlation, how do you test its assumption of normality?

Answer 22

Look at Skewness + Kurtosis values for both variables.

If both in their acceptable ranges = theres normality!

Question 23

Using knowledge of Pearsons Correlation, how do you test its assumption of linearity?

Answer 23

Whether the pattern of scatter plot fits appears to be linear or curved.

Question 24

Using knowledge of Pearsons Correlation, how do you test its assumption of homogeneity of variance?

Answer 24

If by looking at the scatterplot, if the distribution of y-axis values seems similar across the range of x-axis values.

So theres no fanning.

Question 25

Using knowledge of Pearsons Correlation, how do you test its assumption of no obvious outliers?

Answer 25

By looking at the scatterplot