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The two way analysis of variance is an extension of the one way analysis of variance.
Instead of running the test using one independent variable, we’re going to take a look at how
more than one independent variable will be used with this method.
This can make the testing more efficient by taking more information into account.
Once again, we have another research question that we’re going to answer
using an example of a professor’s testing method.
Let’s go ahead and take a look at the data file and begin the testing now.
Once again, we have a hypothetical example to apply to this particular data file.
An essay is given to a college class, but before they were administered the test, the professor asked the students
to rank their typing ability as either no typing ability, some typing ability or highly skilled at typing.
The test was administered in two different methods.
The first half of the class was assigned to write the final with a blue book
and the other half were to type it on notebook computers.
After grading each of the finals, the mean score of each group is examined.
Let’s take a look at the breakdown of our data file.
We see that our first variable is called ability; this accounts for the students input about their own typing ability.
The second variable called method is going to state which test method that particular student was administered.
Did they use the blue book or the notebook computer?
The third and final variable is called score.
This is actual raw score that each of the individuals in the class earned on the exam.
Both primary groups have an even number of students as well as an equal proportion of those students for each
of the three categories that we have created.
What we want to find out is this - will typing ability and test method affect students’ test scores?
Our null hypothesis states typing ability and test method do not affect student test scores
and our alternative hypothesis states that typing ability and test method do affect student test scores.
Let’s begin the analysis by clicking on the analyze menu.
Point to general linear model, then select univariate.
In the univariate dialog box, select the score variable then transfer that to your dependent variable list box.
Then select the ability variable, hold the shift key and also select the method variable,
then move both of these two variables into the fixed factor list box.
Click the options button.
And in the univariate options dialog box, click to check the descriptive statistics option. Click the continue button
Then select the ok button to run your analysis.
Scroll down until you can view the full descriptive statistics table.
By looking at this table, it’s clear that the group of students who performed the best on average were those
who took the test on the computer and had some typing ability.
Now scroll down until you can view the full test of between subjects effects table.
The calculated significance value of .047 is less than the .05 threshold which leads to the rejection of the null hypothesis.
We can therefore conclude that the combination between students’ typing ability
and the test method do indeed affect the students' outcome of their test.