Section 7: basic analysis for determining associations with numeric outcomes II: Scatterplots & correlation analysis

Question 1

What are the statistical tools used for 2 numeric variables?

Answer 1

1. Scatterplot
2. Pearson correlation
3. Spearman rank correlation

Question 2

What is a scatterplot?

Answer 2

• A graphical summary showing how one numeric variable changes with another.
• X-axis: independent variable (exposure)
• Y-axis: dependent variable (outcome)

Question 3

When is a scatterplot usually drawn?

Answer 3

Before working out a linear correlation coefficient or fitting a regression line

Question 4

What does the resulting pattern of a scatterplot indicate?

Answer 4

type & strength of relationship between 2 variables

Question 5

What is the line of best fit?

Answer 5

• Also called a “Trend Line“
• A straight line that best represents the data on a scatter plot

Question 6

What can we interpret from scatterplots?

Answer 6

Info about relationship

• Direction → positive, negative, or none
• Form → linear, nonlinear, clusters
• Strength → weak or strong

Question 7

When can we use pearson correlation analysis?

Answer 7

When relationship between 2 quantitative variables is visually linear, can quantify relationship using pearsons

Question 8

What are the assumptions for pearsons correlation?

Answer 8

1. Relationship appears linear (linearity)
2. Both variables are normally distributed (normality)
3. No outliers
4. Variables have same variance (homoscedasticity)

Question 9

How can we test normality (if variables are normally distributed)?

Answer 9

Shapiro-wilk or shapiro francia tests

Question 10

How do we test homoscedasticity of variance?

Answer 10

2 sample variance comparison test (sdtest) in Stata

Question 11

What does the correlation coefficient show?

Answer 11

It shows strength & direction of relationship between two numeric variables.

Question 12

When do we use Spearman correlation?

Answer 12

When relationship is monotonic (not necessarily linear) or data are not normally distributed.

Question 13

When do we use Pearson correlation?

Answer 13

When relationship between two numeric variables is linear & data are normally distributed.

Question 14

What is the range of the correlation coefficient (r)?

Answer 14

r ranges from –1 to +1.

Question 15

What does the value of r show?

Answer 15

• Strength of the relationship
• Closer r is to –1 or +1, the stronger the association.

Question 16

What does the sign of r indicate?

Answer 16

The direction of the relationship:
* Positive (+): both variables increase together
* Negative (–): one increases while the other decreases

Question 17

What does the p-value in correlation mean?

Answer 17

• It shows the statistical significance
• whether the correlation is likely due to chance or represents a real association.

Question 18

How do we interpret the strength of r?

Answer 18

r Range | Interpretation

0.00–0.20 → Negligible
0.20–0.40 → Weak
0.40–0.60 → Moderate
0.60–0.80 → Strong
0.80–1.00 → Very strong

Question 19

When do we use Spearman Rank Correlation Analysis?

Answer 19

When relationship between 2 quantitative variables is monotonic, but the linearity, normality, or equal variance assumptions are not met.

Question 20

What type of relationship does Spearman correlation measure?

Answer 20

A monotonic relationship — where variables move in same or opposite direction, but not necessarily at a constant rate (not linear).

Question 21

What is the monotonic relationship when it is monotoniocally increasing?

Answer 21

as x variable increases, y variable never decreases

Question 22

What is the monotonic relationship when it is monotoniocally decreasing?

Answer 22

as x variable increases, y variable never increases

Question 23

What is the monotonic relationship when it is not monotonic?

Answer 23

as x variable increases, y variable sometimes decreases & sometimes increases

Question 24

What is Spearman’s Rank Correlation Analysis?

Answer 24

A non-parametric test that measures strength & direction of **monotonic** relationship between two numeric (or ordinal) variables.

Question 25

When is spearman rank correlation done?

Answer 25

* Between two numeric variables when at least one of the two is not normally distributed * Also possible when one of the two variables is ordinal categorical

Question 26

What is a monotonic relationship?

Answer 26

Relationship where as one variable increases, other consistently increases or decreases, but not necessarily in a straight line.

Question 27

When is Spearman’s correlation used instead of Pearson’s?

Answer 27

When data are **not normally distributed**, relationship is **nonlinear but monotonic**, or the assumptions of l**inearity & equal variance** aren't met.

Question 28

What is the symbol for Spearman’s Rank Correlation Coefficient?

Answer 28

ρ (rho)

Question 29

What does Spearman Rank Correlation Coefficient indicate?

Answer 29

direction & strength of monotonic relationship

Question 31

What does a positive Spearman’s ρ indicate?

Answer 31

* As one variable increases, the other also increases — their ranks move in the same direction. 📈 Example: As hours of study increase, exam scores increase. 👉 Perfect positive = ρ = +1

Question 32

What does a negative Spearman’s ρ indicate?

Answer 32

* As one variable increases, the other decreases — their ranks move in **opposite** directions. 📉 Example: As physical activity increases, body weight decreases. 👉 Perfect negative = ρ = –1

Question 33

What does Spearman’s ρ = 0 mean?

Answer 33

* No monotonic relationship * changes in one variable do not consistently relate to changes in the other.