**When do we do ANOVA?**

ANOVA stands for ANalysis Of VAriance. We run ANOVA when we want to compare the mean scores of three of more groups.

**Example Scenario**

In a statistics course, a group of psychology students were assigned to three different tutorial groups taught by three different tutors, Gary, Janni and Jin. We want to see if the students taught by different tutors did equally well at the end semester exams.

In this example, our null hypothesis is that the mean exam scores of students from different groups are the same. Our alternative hypothesis is that the mean scores of students from different groups are NOT all the same. (However, we can't tell where the difference is from ANOVA with further analysis). The dataset can be obtained here.

In the data, the first column is exam scores for all students and the second column is tutor. There are a few different ways to perform one-way ANOVA in PASW (SPSS) that yield the same result . In this tutorial, I will use the general linear model approach.

**Step 1**

Select "Analyze -> General Linear Model -> Univariate".

A new window pops out.

**Step 2**

From the list on the left, select the variable "Scores" as "Dependent Variable" and the variable "Tutor" as the "Fixed Factor(s)". Click "OK".

**Step 3**

The results now pop out in the "Output" window.

**Step 4**

We can now interpret the result.

To see if the mean scores of students from different tutorials are the same, we can look at the third rows of the second table. From A, since the p-value is 0.237, we reject the alternative hypothesis and conclude that the mean scores of students from different tutorials are the same at 5% significant level.

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