correlation

Question 1

Correlation

📊 What is Correlation?

Answer 1

• measures the form,direction, & magnitude of the relationship between two continuous variables
• uses two two internal/ ratio type variables
• ex.). Do hours studied relate to exam score?

helps understand whether variables change togther.

Form: understood by scatterplot
direction: ➕ 📈 / ➖📉 / 0 ░
magnitude:

Question 2

correlation

🦜What does the correlation coefficient (r) measure?

Answer 2

• measures the strength and direction of the linear relationship between two variables

range: r always falls between -1.00 & +1.00

• direction: positive or negative
• strenght: how cose the value is to 0 (weak) or to +/- 1 (strong)

Question 3

correlation

🔑 What are the properties of the correlation coefficient?

(three qualities)

Answer 3

form

Direction:
- Positive (+): variables move in the same direction
- Negative (-): one increases ⬆️ while the other decreases⬇️
- zero: no linear relationship
Form
- measures linear relationships
magnitude
- strength of the relationship (closer to +/-1 = stronger)

Question 4

What is the difference between positive, negative, and no correlation?

Answer 4

➕📈Positive correlation:
- As one variable increases, the other also increases.
- scatterplot slopes upward
**ex) **
- Hours studied ⬆️ Exam score⬆️
- salary ⬇️ job satisfaction⬇️
-self-esteem ⬆️ body satisfaction⬆️

➖📉 Negative correlation: ⬆️⬇️
- As one variable increases, the other decreases.
- scatterplot slopes downward
ex.)
-hrs procrastinating ⬆️ Exam score⬇️
- pain⬆️ hapiness⬇️
- self-esteem⬇️ sadness⬆️
- scatterplot looks random
0️⃣ ░ No correlation
- no relationship… two variables not related
- ex.)
- hrs of procrasti - numbers of hairs
- pain - # of snickers on halloween

Question 5

How do you interpret the magnitude and direction of a correlation?

Answer 5

magnitude (strength):
- small = 0.2
- medium- 0.5
- large > 0.6
- (closer to +/- = stronger relationship)
- (context matters– what counts as “stong” depends on the field)
- looking at graph:
- strong relationship = scatter plots tighter- linear line is visblie
- weak relationship = liear line still visible– scatterplots looser
Direction:
- positive–> both variables move together
- negative –> variables movie in opposite directions
- zero –> no relationship

ex.)
r= 0.7: strong positive correlation
r= -0.30: weak negative correlation
r= 0.00: no correlation

Question 6

📊 Using a Correlation Table

Answer 6

• Degrees of freedom (df): n-2.
• Critical value: Look up in Pearson’s r table for chosen alpha (e.g., 0.05).
  - Decision rule:
• If |r| ≥ critical value → reject null hypothesis (significant correlation).
• If |r| < critical value → fail to reject null (not significant)

Question 7

Why does correlation not mean causation?

Answer 7

Correlation only shows association not cause- & effect

ex.) - Example: Ice cream sales and sunburns are correlated, but hot weather causes both.

Question 8

What is spurious correlation?

Answer 8

A misleading correlation caused by coincidence or a third variable

ex. nicolas cage films vs. swimming pool drownings