4.12.5 Hypothesis Testing for Correlation

What is a hypothesis test for correlation?

• You can use a t-test to test whether there is linear correlation between two normally distributed variables
• If specifically testing for positive (or negative) linear correlation then a one-tailed test is used
• If testing for any linear correlation then a two-tailed test is used
• A sample will be taken and the raw data will be given
• You might be asked to calculate the PMCC (Pearson's product-moment correlation coefficient)

What are the steps for a hypothesis test for correlation?

• STEP 1: Write the hypotheses
  • H₀ : ρ = 0
    • Clearly state that ρ represents population correlation coefficient between the two variables
    • In words this means there is no correlation
  • H₁ : ρ < 0, H₁ : ρ > 0 or H₁ : ρ ≠ 0

• STEP 2: Calculate the p-value or the PMCC
• Choose a t-test for linear regression
• Enter the data as two lists into GDC
• STEP 3: Decide whether there is evidence to reject the null hypothesis
• If the p-value < significance level then reject H₀
• If the absolute value of the PMCC is bigger than the absolute value of the critical value then reject H₀
• If you are expected to use the PMCC you will be given the critical value in the exam
• STEP 4: Write your conclusion
• If you reject H₀­ then there is evidence to suggest that...
• There is a negative linear correlation between the two variables (for H₁ : ρ < 0)
• There is a positive linear correlation between the two variables (for H₁ : ρ > 0)
• There is a linear correlation between the two variables (for H₁ : ρ ≠ 0)
• If you accept H­₀ then there is insufficient evidence to reject the null hypothesis which suggests that...
• There is not a negative linear correlation between the two variables (for H₁ : ρ < 0)
• There is not a positive linear correlation between the two variables (for H₁ : ρ > 0)
• There is not a linear correlation between the two variables (for H₁ : ρ ≠ 0)