Question

A social psychologist hypothesizes that using Facebook is related to depression. The psychologist collects hours on Facebook and depression score data from a sample of depression patients from a clinic. What can the psychologist conclude with α = 0.05?

Facebook	Depression
3 3 4 5 4 3 4 2 3	4 0 4 9 6 1 11 2 5

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected above:

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

There is a significant positive relationship between using Facebook and depression.There is a significant negative relationship between using Facebook and depression.    There is no significant relationship between using Facebook and depression.

Answer 1

a)

Correlation Coefficient

b)

n(Σxy) - (Σx)(Σy) [nΣχ2 - (Σκ)?][ηΣy2 - (Σy)2]

Using the above formulae and the given values we get,

r = 0.72

Correlation Hypothesis Test

Alpha = 0.05

Null and Alternate Hypothesis

H₀: ρ = 0 (No Correlation)

H_a: ρ <> 0 (Correlation is present)

Test Statistic

t = r* (n-2)^1/2/(1-r²)^1/2 = 0.72 *(9-2)^1/2 /(1-0.72²)^1/2 = 2.75

p-value = TDIST(2.75,9-2,2) = 0.028

Result

Since the p-value is less than 0.05, we reject the null hypothesis.

c)

effect size = r = 0.72

Since r is greater than 0.7, hence it is Large effect

d)

There is a significant positive relationship between using Facebook and depression