Correlation Homework

Question

A researcher is interested in how time spent on social media is related to self-esteem. He has participants how much time they spend on social media per day and has them take a self-esteem scale (on an 11 point scale). The data is as follows:

Participant	Hours per day on social media	Self-esteem score
A	7	4
B	4	7
C	8	9
D	3	10
E	6	8
F	2	11
G	3	10
H	5	5

a. Who are the groups being tested?

b. What are the null and research hypotheses?

c. What is the mean of X?

What is the mean of Y?

Find the deviances for both groups. (X – My) and (Y – My)

Multiply the deviances like in the lecture

Sum these.

What number do you get? ___________________________

This is the numerator

Square the deviances in X and Y

What is the Sum of Squares of X?

What is the Sum of Squares of Y?

What do you get when you multiply SSx and SSy? _______________________________

Take the square root of that ____________________________

This is your denominator

d. What is r? ______________________

e. What is the critical value? ___________________________________

f. What is your decision? ______________________________

Answer 1

Hi Alexis,

Here’s what it looks like step by step.

The mean hours on social media is 4.75, and the mean self-esteem score is 8.

If we take Participant A (7 hours, score 4) as an example:

1. Deviation for X: 7 − 4.75 = +2.25
2. Deviation for Y: 4 − 8 = −4
3. Multiply them: 2.25 × (−4) = −9

You repeat this for everyone, add them all up, and that total is your numerator (−21). The denominator (from the sums of squares) works out to about 37.23.

So r = −21 ÷ 37.23 ≈ −0.56. That shows a moderate negative relationship: more social media time tends to go with lower self-esteem.

With only 8 participants, the critical value is about ±0.707. Since −0.56 doesn’t reach that, we fail to reject the null; the trend is there, but not statistically significant in this small sample.

A quick scatterplot will make this really clear; you’ll see the downward pattern, but also how one or two points have a big impact.