A Critical Values Of The Pearson Correlation Coefficient R NOTE: To Test Ho: P= 0 Jagainst Hi: P*0, Reject Ho If The Absolute Value Of Ris Greater Than The Critical Value In The Table. 0.602 Critical Values Of The Pearson Correlation Coefficient A = 0.05 A = 0.01 0.950 0.990 0.878 0.959 10.811 0.917 0.754 10.875 0.707 0.834 0.666 0.798 0.632 0.765 10.735
The Correct Answer and Explanation is :
The Pearson correlation coefficient (r) is a statistical measure used to evaluate the strength and direction of the linear relationship between two variables. The null hypothesis (H0) for a correlation test typically states that there is no relationship between the variables, i.e., ρ = 0, where ρ is the population correlation coefficient. The alternative hypothesis (Ha) asserts that ρ ≠ 0, meaning there is some significant linear relationship.
Critical Values of the Pearson Correlation Coefficient:
The table you’ve provided includes the critical values of Pearson’s correlation coefficient (r) at two significance levels (α = 0.05 and α = 0.01). These critical values are used to determine whether the observed correlation coefficient is significantly different from zero, which would indicate a significant linear relationship between the variables.
- Significance level α = 0.05: This means there’s a 5% chance of rejecting the null hypothesis if it is true.
- Significance level α = 0.01: This is a more stringent threshold, meaning there’s only a 1% chance of a Type I error.
How to Use the Critical Values:
To test whether the observed correlation coefficient (r) is significant, you compare it to the critical values at the chosen significance level. The process is as follows:
- State the hypotheses:
- H0: ρ = 0 (no linear relationship).
- Ha: ρ ≠ 0 (there is a linear relationship).
- Compute the Pearson correlation coefficient (r) based on the sample data.
- Find the appropriate critical value from the table corresponding to the sample size and the chosen significance level (α = 0.05 or α = 0.01).
- Decision rule:
- If the absolute value of the computed r is greater than the critical value, reject the null hypothesis (H0) in favor of the alternative hypothesis (Ha).
- If the absolute value of r is less than or equal to the critical value, fail to reject the null hypothesis.
Example:
If your computed r value is 0.85 with a sample size of 20 and you’re testing at α = 0.05, you would compare it to the critical value of 0.602 (based on the table for n = 20). Since 0.85 > 0.602, you would reject the null hypothesis and conclude that there is a significant linear relationship between the two variables.
Conclusion:
The critical values of the Pearson correlation coefficient are essential tools for hypothesis testing, helping to assess whether a significant linear relationship exists between two variables. By comparing the observed r value with the critical values at different significance levels, researchers can make informed decisions about the relationship between variables in their data.