Chapter 12: Correlation

Question 1

What is correlation:

A: Correlation is a measure of causation, indicating the direct influence of one variable on another in a statistical analysis.

B: Correlation is a common statistical technique for
describing associations or trends between two
variables

C: Correlation is exclusively used to determine the strength of relationships between multiple variables within a dataset, disregarding any trends or associations between just two variables.

Answer 1

B: Correlation is a common statistical technique for
describing associations or trends between two
variables

The use of “correlation” conveys the idea that two
events tend to happen together (if A happens, then B happens).

Question 2

Pearson’s correlation is the most common correlation in psychology research, when should you use it?

A: Correlation is used to evaluate an association
between two categorical variables

B: Correlation is used to evaluate an association
between two numeric variables

C: Correlation is used to evaluate an association
between a categorical variable and a
numeric variable (e.g., treatment vs. control
group comparison).

Answer 2

B: Correlation is used to evaluate an association
between two NUMERIC variables

> The SAMPLE Pearson’s correlation is denoted as r

Question 3

REVIEW: Which test is used to measure the relationship between one categorical variable and one numeric variable? Select all that apply:

A. ANOVA
B. Independent-sample t-test
C. Correlation

Answer 3

A. ANOVA
B. Independent-sample t-test

Question 4

True or false: Scale scores are numerical variables?

A: True

B: False

Answer 4

A: True

Question 5

How many scores does correlation require from each participant:

A: 1

B: 2

C: It varies from study to study

Answer 5

B: 2

> AND both must be numeric!

Question 6

What is a scatterplot?

A: A scatterplot is a graphical representation used exclusively for categorical data, where each category is represented by a distinct shape or symbol on a coordinate system.

B: Scatterplots are only applicable when there is a perfect linear relationship between variables, and they cannot be used to visualize any other type of association or pattern.

C: A scatterplot helps visualize a correlation.
One variable will be on the horizontal
axis (x-axis) and the other variable will be on the
vertical axis (y-axis). A dot denotes the location of each score pair in a coordinate system.

Answer 6

C: A scatterplot helps visualize a correlation.
One variable will be on the horizontal
axis (x-axis) and the other variable will be on the
vertical axis (y-axis). A dot denotes the location of each score pair in a coordinate system.

Question 7

Anatomy Of A Scatterplot - ADD THIS SLIDE TO YOUR CHEAT SHEET (SLIDE 11)

Answer 7

Anatomy Of A Scatterplot - ADD THIS SLIDE TO YOUR CHEAT SHEET (SLIDE 11)

Question 8

What are the characteristics of a correlation:

A:
1. Correlations have the same direction and strength
2. The direction can be positive or negative
3. The strength of a correlation can range from
weak (or nonexistent) to strong (or perfect)

B:
1. Correlations have the same direction but differ in strength
2. The direction is almost always positive
3. The strength of a correlation can range from
weak (or nonexistent) to strong (or perfect)

C:
1. Correlations differ in direction and strength
2. The direction can be positive or negative
3. The strength of a correlation can range from
weak (or nonexistent) to strong (or perfect)

Answer 8

C:
1. Correlations differ in direction and strength
2. The direction can be positive or negative
3. The strength of a correlation can range from
weak (or nonexistent) to strong (or perfect)

Question 9

Describe a positive correlation:

A: Scores on the two variables tend to move in the
same direction or follow the same trend (a high score on one variable tends to be associated with a high score on the other variable, and a low score tends to be paired with a low score).

B: In a positive correlation, scores on the two variables move in opposite directions, meaning a high score on one variable is associated with a low score on the other variable.

C: A positive correlation indicates that there is no discernible relationship between the two variables, and scores on one variable do not influence or predict scores on the other variable.

Answer 9

A: Scores on the two variables tend to move in the
same direction or follow the same trend (a high score on one variable tends to be associated with a high score on the other variable, and a low score tends to be paired with a low score).

FOR EXAMPLE:
More time studying = higher exam grade
Less time studying = lower exam grade

SHE MIGHT ALSO SAY:
A high score on the independent variable tends to be associated with a high score on the dependent variable

> You’ll see more dots in the green areas of the “Anatomy Of A Scatterplot” image on slide 11

> If you think it will be helpful, add the image from slide 26 to your cheat sheet!!!

Question 10

Describe a negative correlation:

A: In a negative correlation, scores on the two variables move in the same direction, meaning a high score on one variable is associated with a high score on the other variable.

B: A negative correlation implies that there is no relationship between the two variables, and the scores on one variable have no impact on or connection to the scores on the other variable.

C: Scores on the two variables tend to move in the
opposite direction or follow the opposite trend (a high score on one variable tends to be associated with a low score on the other variable (and vice versa).

Answer 10

C: Scores on the two variables tend to move in the
opposite direction or follow the opposite trend (a high score on one variable tends to be associated with a low score on the other variable (and vice versa).

FOR EXAMPLE:
More unhealthy food = less healthy
Less unhealthy food = more healthy

SHE MIGHT ALSO SAY:
A high score on the independent variable tends to be associated with a low score on the dependent variable

> You’ll see more dots in the red areas of the “Anatomy Of A Scatterplot” image on slide 11

> If you think it will be helpful, add the image from slide 28 to your cheat sheet!!!

Question 11

Pearson’s correlation quantifies the magnitude
of a correlation on a _____ to ______ scale:

A: 1, -1

B: Linear

C: 0, 1

Answer 11

C: 0, 1

> POSITIVE correlations range between 0 (no
correlation) and 1 (perfect positive correlation)

> NEGATIVE correlations range between 0 (no
correlation) and -1 (perfect negative correlation)

Question 12

Based on the scatterplot from slide 31, is the correlation positive or negative?

A. Positive
B. Negative

Answer 12

A. Positive

Question 13

True or false: Pearson’s correlation is an effect size. We don’t need to standardize it?

A: True

B: False

Answer 13

A: True

> It’s like Cohen’s D effect size in that respect

> There is no absolute value for Pearson’s correlation

> The range can only be between -1 and 1

> If the value given is exactly on the threshold (.30 for example) go with the larger value (so .30 would be moderate not small).

> When talking about the MAGNITUDE use the absolute value otherwise don’t use the absolute value (the signs only tell you the direction).

!!!ADD SLIDE 34 TO YOUR CHEAT SHEET!!!!

Question 14

IF YOU’D LIKE TO HAVE SOME VISUAL EXAMPLES OF NEGLIGIBLE-LARGE CORRELATIONS YOU CAN ADD SLIDES 35-39!

Answer 14

IF YOU’D LIKE TO HAVE SOME VISUAL EXAMPLES OF NEGLIGIBLE-LARGE CORRELATIONS YOU CAN ADD SLIDES 35-39!

Question 15

What values represent Pearson correlation effect size represents a perfect correlation?

A: 1

B: 1.00, -1.00

C: 0

Answer 15

B: 1.00, -1.00

> THERE’S AN IMAGE OF THIS ON SLIDE 39 IF YOU THINK IT WILL BE HELPFUL FOR YOU!

Question 16

Based on the scatterplot on slide 40, how strong is the correlation?

A. Negligible
B. Small
C. Moderate
D. Large
E. It is hard to tell

Answer 16

A. Negligible
B. Small

Question 17

After calculating the correlation (represented at “Pearson’s r” on slide 45), how strong is the correlation?

A. Negligible
B. Small
C. Moderate
D. Large
E. It is hard to tell

Answer 17

B. Small

Question 18

LOOK AT SLIDE 45, IF YOU SEE A LINE (—) ON JAMOVI IT MEANS THERE IS NO CORRELATION BETWEEN THE TWO VARIABLES.

IF YOU SEE AN EMPTY SPACE IT MEANS THAT THE VALUE HAS ALREADY BEEN CALCULATED SOMEWHERE ELSE IN THE CHART!

Answer 18

LOOK AT SLIDE 45, IF YOU SEE A LINE (—) ON JAMOVI IT MEANS THERE IS NO CORRELATION BETWEEN THE TWO VARIABLES.

IF YOU SEE AN EMPTY SPACE IT MEANS THAT THE VALUE HAS ALREADY BEEN CALCULATED SOMEWHERE ELSE IN THE CHART!

Question 18

Correlation Interpretation

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Answer 18

The sign of the correlation is positive, meaning that higher levels of narcissism are associated with more selfie posts.

The magnitude (absolute value) of the correlation (.141) is consistent with what psychologists consider a small association.

> Always look for two things in an interpretation:
1. The sign
2. The magnitude (absolute value)

> The sign tells direction / absolute value tells you the magnitude

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Question 18

Here is an incorrect correlation interpretation

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Answer 18

Pearson’s r is not a percentage, it is incorrect to say that there is a 30% relationship, the dependent variable can be predicted with 30% accuracy, etc.

Correlations are not on a ratio scale, so a correlation of .30 is not twice as strong as .15

> No equal distance property

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Question 19

True or false: A zero correlation implies a lack of
association.

A: True

B: False

Answer 19

B: False

A zero correlation may or may not imply a lack of
association. Pearson’s r cannot quantify nonlinear relations.

Question 20

Correlation, Prediction & Causation:

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Answer 20

Correlations make it possible to use the value of one variable to predict the value of another.

For example, self-objectification and narcissism predicted time spent on SNSs; fingers stained yellow
predicts the future development of lung cancer.

Any type of correlation can be used to make a prediction. However, correlation does not imply causation (the underlying cause of the relationship), nor does it tell us why two variables are correlated.

> Basically, you can only say that something “predicts” something but never that it’s the “cause” of something.

> Correlation only tells you something about the relationships between two variables

> With this technique you can say that mathematically, A can predict B, and B can predict A

> The underlying reason for a correlation does not matter in making a prediction. As long as the correlation is stable–lasting into the future–one can use it to make predictions.

> A causal conclusion is more difficult than coming up with a prediction and a prediction has nothing to do with a causal conclusion.

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Question 21

Suppose we find a positive correlation between marital satisfaction and social support from friends and family. If we know someone’s marital satisfaction, can we predict their social support level?

A. Yes
B. No

Answer 21

A. Yes

Question 22

Suppose we find a positive correlation between marital
satisfaction and social support from friends and family. What can we conclude?

A. A higher marital satisfaction leads to higher social support

B. A higher social support level leads to higher marital
satisfaction

C. We lack knowledge about the underlying causal
relationship

Answer 22

C. We lack knowledge about the underlying causal
relationship

> “Leads to” means “causes” and we can NEVER say “causes.”

Question 23

No Correlation ≠ Independence:

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Answer 23

A zero or low correlation does not necessarily mean that two variables are unrelated (uncorrelated).

Pearson’s correlation is limited to linear trends and does a poor job of detecting nonlinear associations (e.g., a line that goes up then down).

> Independence = unrelated to…..

Question 24

Describe a nonlinear relationship:

A: A line that shows an increase up to a certain point but then begins to decrease. It will look like an inverted U.

B: A nonlinear relationship is characterized by a perfectly straight line on a graph, indicating a constant and unchanging association between two variables.

C: In a nonlinear relationship, the line on the graph always slopes downward, suggesting a continuous decrease with no points of increase or turning.

Answer 24

A: A line that shows an increase up to a certain point but then begins to decrease. It will look like an inverted U.

> THERE’S AN IMAGE ON SLIDE 59 IF YOU THINK IT WILL BE HELPFUL!

Question 25

How large is the Pearson’s correlation in the example on slide 59?

A. Negligible
B. Small
C. Moderate
D. Large

Answer 25

A. Negligible

> Pearson’s correlation is limited to linear trends and does a poor job of detecting nonlinear associations (e.g., a line that goes up then down).

> You cannot conclude that these two variables are independent or unrelated.

> Technically for this image we could draw a straight line to help us visualize the Pearson’s correlation better

> The Pearson’s correlation for slide 59 is -.06, although a strong nonlinear relation is visually evident.

Question 26

What is an outlier?

A: Outliers have no effect on the correlation between variables; they are merely data points that can be ignored when analyzing relationships.

B: Outliers (extreme scores) can have a substantial
impact on the correlation. The correlation can increase or decrease, depending on the location of the outlier. Scatterplots are useful for detecting outliers.

C: In a correlation analysis, outliers consistently increase the strength of the correlation, making it a more reliable measure of the relationship between variables.

Answer 26

B: Outliers (extreme scores) can have a substantial
impact on the correlation. The correlation can increase or decrease, depending on the location of the outlier. Scatterplots are useful for detecting outliers.

Question 27

What is the Pearson’s correlation on the right
side of slide 64?

A. -0.2
B. 0.2

Answer 27

A. -0.2

> Changing one data point drastically changes the outcome of the data.

> Everything depends on the location of the outlier

> Correlation is highly sensitive to the location of the outlier

THERE ARE SOME VISUALS OF THIS ON SLIDE 64, AS WELL AS SLIDES 66-67 IF YOU THINK IT MIGHT BE HELPFUL FOR YOU!!!

Question 28

What is a correlation matrix (matrices)?

A: A correlation matrix only displays the mean scores of each variable, providing a summary of the average relationship between them without considering individual data points.

B: Researchers generally examine correlations
among several variables. A correlation matrix is a grid that displays correlations among several variables.
Each variable appears in a row and a column.

C: In a correlation matrix, variables are arranged randomly without any specific order, and the values in the matrix represent the differences between variables rather than their correlations.

Answer 28

B: Researchers generally examine correlations
among several variables. A correlation matrix is a grid that displays correlations among several variables.
Each variable appears in a row and a column.

> They show two numerical variables pair-by-pair (all correlations for every pair)

THERE’S AN IMAGE OF THIS ON SLIDE 70 IF YOU THINK IT WILL BE HELPFUL FOR YOU!!!

Question 29

What is a correlation null hypothesis?

A: The correlation null hypothesis proposes that the population correlation is always positive, regardless of the sample data.

B: The null hypothesis predicts that the population
correlation (ρ) is zero.

C: In a correlation null hypothesis, the expected correlation in the population is equal to the sample correlation, ensuring that there is no deviation between the two.

Answer 29

B: The null hypothesis predicts that the population
correlation (ρ) is zero.

ρ = the Greek letter “rho.”

Here’s the formula:
Ho: ρ = 0

“POPULATION Pearson’s correlation is zero” means that the two variables are not linearly associated in the population.

Question 30

What is a correlation alternate hypothesis?

A: An alternate hypothesis for correlation always assumes a two-tailed test, stating that the correlation is equal to zero.

B: In a correlation alternate hypothesis, a two-tailed test can only specify that the correlation is exactly zero, providing no information about whether it is larger or smaller.

C: A one-tailed hypothesis specifies that the
correlation is larger than zero or smaller than zero. A two-tailed hypothesis specifies that the correlation is not equal to zero.

Answer 30

C: A one-tailed hypothesis specifies that the
correlation is larger than zero or smaller than zero. A two-tailed hypothesis specifies that the correlation is not equal to zero.

One-tailed hypothesis formulas:
Ha : ρ > 0 OR Ha : ρ < 0

Two-tailed hypothesis formula:
Ha : ρ ≠ 0

Question 31

Significance Testing (p-value):

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Answer 31

The hypothesis testing process of correlation is relatively complex.

p-values less than .05 are “statistically significant”, meaning that we can reject the null hypothesis and there is likely a reliable linear association.

> No linear relation (reject) vs. linear relation (fail to reject).

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Question 32

Probability (p-value) Interpretation:

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Answer 32

The p-value is < .001

If the population correlation is truly zero (the null is
true), the probability of drawing a sample that gives a
correlation of ± .14 or more extreme is smaller than
0.001

p-values less than .05 (p < .05) provide evidence against
the null hypothesis

The result was significant, meaning that there is likely a small linear relation between the number of selfies posted and narcissism

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Question 33

What is our conclusion based on everything we know from slide 76?

A. We can reject the null hypothesis that the population correlation is zero

B. We fail to reject the null hypothesis that the
population correlation is zero

Answer 33

A. We can reject the null hypothesis that the population correlation is zero

Question 34

APA-Style Results Summary:

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Answer 34

LINE 1 (What you did in the study):
We performed a correlation analysis to assess the linear relation between the number of selfies posted and narcissism.

LINE 2 (Descriptive Statistics):
Table 1 gives the means and standard deviations for each variable.

LINE 3 (Statistical significance):
The analysis revealed that the number of selfies posted and narcissism are statistically linearly related, r = .141, p < .001.

LINE 4 (Effect size):
Further, the correlation effect size indicated a small effect by conventional standards

> Report Correlation Table If Multiple Correlation Tests Are Conducted