Lab 23
Regression & Correlation as
hypothesis tests
It turns out that in addition to
the 4 statistical tests we've learned so far, you already know 2 more.
Remember regression and correlation? Those can be considered hypothesis
tests, too.
For regression, the null hypothesis is that population parameter for the regression coefficient (b) is 0.
For correlation, the null hypothesis is that r (actually ρ, the Greek letter rho, for the population parameter) is 0.
The computation for these tests is not necesary for this course but you should know that they are t-tests just like others.
The population parameter is expected to be 0 if the null hypothesis is true. The standard error of b has a formula but we won't be concerned with it.
The results of a correlation hypothesis test and simple regression hypothesis test will be exactly the same (i.e., the p-value is the same. In addition, the standardized regression coefficient (beta or β) is exactly the same as the correlation coefficient.
The choice between correlation and simple regression a matter of emphasis. Regression is more for prediction and correlation is more for measuring the strength of the relationship between 2 variables in an easy-to-understand metric. Even so, the distinction is not that important for this course. In more advanced courses, you'll learn about multiple regression (more than 1 predictor) and you'll see that multiple regression and correlation are still related but have important differences.
In SPSS, the p-value for a test of the correlation coefficient is found below the correlation coefficient as depicted below:
For regression, the p-value, the t-test, and standard error are found here:
Download the worksheet here to answer the questions.
Email it to your GA when you are finished.
For regression, the null hypothesis is that population parameter for the regression coefficient (b) is 0.
For correlation, the null hypothesis is that r (actually ρ, the Greek letter rho, for the population parameter) is 0.
The computation for these tests is not necesary for this course but you should know that they are t-tests just like others.
The population parameter is expected to be 0 if the null hypothesis is true. The standard error of b has a formula but we won't be concerned with it.
The results of a correlation hypothesis test and simple regression hypothesis test will be exactly the same (i.e., the p-value is the same. In addition, the standardized regression coefficient (beta or β) is exactly the same as the correlation coefficient.
The choice between correlation and simple regression a matter of emphasis. Regression is more for prediction and correlation is more for measuring the strength of the relationship between 2 variables in an easy-to-understand metric. Even so, the distinction is not that important for this course. In more advanced courses, you'll learn about multiple regression (more than 1 predictor) and you'll see that multiple regression and correlation are still related but have important differences.
In SPSS, the p-value for a test of the correlation coefficient is found below the correlation coefficient as depicted below:
For regression, the p-value, the t-test, and standard error are found here:
Download the worksheet here to answer the questions.
Email it to your GA when you are finished.