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
  • H_0?:?ρ?= 0
    • Clearly state that?ρ?represents?population correlation coefficient?between the two variables
    • In words this means there is no correlation
  • H_1?:?ρ?< 0, H_1?:?ρ?> 0 or H_1?:?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 H_1?:?ρ?< 0)
    • There is a positive linear correlation between the two variables (for H_1?:?ρ?> 0)
    • There is a linear correlation between the two variables (for H_1?:?ρ?≠ 0)
  • If you?accept H-_0?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 H_1?:?ρ?< 0)
    • There is not a positive linear correlation between the two variables (for H_1?:?ρ?> 0)
    • There is not a linear correlation between the two variables (for H_1?:?ρ?≠ 0)