*32*

AÂ one-way ANOVAÂ is used to determine whether or not different levels of an explanatory variable lead to statistically different results in some response variable.

For example, we might be interested in understanding whether or not three levels of education (Associateâ€™s degree, Bachelorâ€™s degree, Masterâ€™s degree) lead to statistically different annual incomes. In this case, we have one explanatory variable and one response variable.

**Explanatory variable:**Â level of education**Response variable:**Â annual income

AÂ **MANOVA**Â is an extension of the one-way ANOVA in which there is more than one response variable. For example, we might be interested in understanding whether or not level of education leads to different annual incomesÂ *andÂ *different amounts of student loan debt. In this case, we have one explanatory variable and two response variables:

**Explanatory variable:**Â level of education**Response variables:**Â annual income, student loan debt

Because we have more than one response variable, it would be appropriate to use a MANOVA in this case.

In this tutorial, weâ€™ll explain how to perform a MANOVA in SPSS.

**Example: MANOVA in SPSS**

To illustrate how to perform a MANOVA in SPSS, weâ€™ll use the following dataset that contains the following three variables for 24 individuals:

**educ:Â**level of education (0 = Associate, 1 = Bachelor, 2 = Master)**income:Â**annual income**debt:Â**total student loan debt

Use the following steps to perform a MANOVA in SPSS:

**Step 1: Perform a MANOVA.**

Click theÂ **AnalyzeÂ **tab, thenÂ **General Linear Model**, thenÂ **Multivariate**:

In the new window that pops up, drag the variablesÂ **incomeÂ **andÂ **debtÂ **into the box labelled Dependent Variables. Then drag the factor variableÂ **educationÂ **into the box labelled Fixed Factors:

Next, click the buttonÂ **Post Hoc**. Drag the factorÂ **educationÂ **into the box labelledÂ **Post Hoc Tests for**. Then check the box next toÂ **Tukey**. Then clickÂ **Continue**.

Lastly, clickÂ **OK**.

**Step 2: Interpret the results.**

Once you clickÂ **OK**, the results of the MANOVA will appear. Here is how to interpret the output:

**Multivariate Tests**

This table tells you whether or notÂ Â level of education leads to statistically significant differences in annual income and total student debt. We will look at the numbers in the row titledÂ **Wilksâ€™ Lambda**:

The overall F statistic isÂ **6.138Â **and the corresponding p-value isÂ **.001**. Since this value is less than .05, this indicates that level of education does have a significant effect on annual income and total student debt.

**Tests of Between-Subjects Effects**

This table shows the individual p-values for bothÂ **incomeÂ **andÂ **debt**:

The p-value for income isÂ **.003Â **and the p-value for debt isÂ **.000**. Since both of these values are less than .05, it means that level of education has a statistically significant effect on both income and debt.

**Post Hoc Tests**

This table displays the Tukey post hoc comparisons for each level of education.

From the table we can observe the following:

- The amount of income for individuals with an Associateâ€™s degree (education=0) is significantly different than the amount of income for individuals with a Masterâ€™s degree (education=1) |Â
**p-value = .003**. - The amount of income for individuals with a Bachelorâ€™s degree (education=1) is significantly different than the amount of income for individuals with a Masterâ€™s degree (education=2) |Â
**p-value = .029**. - The amount of income for individuals with an Associateâ€™s degree (education=0) is significantly different than the amount of income forÂ individuals with a Bachelorâ€™s degree (education=1) |Â
**p-value = .018**. - The amount of income for individuals with an Associateâ€™s degree (education=0) is significantly different than the amount of income forÂ individuals with a Masterâ€™s degree (education=2) |Â
**p-value = .000**.

**Further Reading:Â **The Differences Between ANOVA, ANCOVA, MANOVA, and MANCOVA