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AÂ two-way ANOVAÂ is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups that have been split on two factors.

The purpose of a two-way ANOVA is to determine how two factors impact a response variable, and to determine whether or not there is an interaction between the two factors on the response variable.

This tutorial explains how to conduct a two-way ANOVA in SPSS.

**Example: Two-Way ANOVA in SPSS**

A botanist wants to know whether or not plant growth is influenced by sunlight exposure and watering frequency. She plants 30 seeds and lets them grow for two months under different conditions for sunlight exposure and watering frequency. After two months, she records the height of each plant, in inches.

The results are shown below:

Use the following steps to perform a two-way ANOVA to determine if watering frequency and sunlight exposure have a significant effect on plant growth, and to determine if there is any interaction effect between watering frequency and sunlight exposure.

**Step 1: Perform the two-way ANOVA.**

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

Drag the response variableÂ **heightÂ **into the box labelledÂ Dependent variable. Drag the two factor variables **waterÂ **andÂ **sunÂ **into the box labelled Fixed Factor:

Next, click theÂ **PlotsÂ **button. DragÂ **waterÂ **into the box labelled Horizontal axis andÂ **sunÂ **into the box labelled Separate lines. Then clickÂ **Add**. The words **water*sunÂ **will appear in the box labelled Plots.Â Then clickÂ **Continue**.

Next, click theÂ **Post HocÂ **button. In the new window that pops up, drag the variableÂ **sunÂ **into the box labelled Post Hoc Tests for. Then check the box next toÂ **Tukey**. Then clickÂ **Continue**.

Next, click theÂ **EM MeansÂ **button. Drag the following variables into the box labelled Display Means for. Then clickÂ **Continue**.

Lastly, clickÂ **OK**.

**Step 2: Interpret the results.**

Once you clickÂ **OK**, the results of the two-way ANOVA will appear. Here is how to interpret the results:

**Tests of Between-Subjects Effects**

The first table displays the p-values for the factorsÂ **waterÂ **andÂ **sun**, along with the interaction effectÂ **water*sun**:

We can see the following p-values for each of the factors in the table:

**water:Â**p-value = .000**sun:Â**p-value = .000**water*sun:Â**p-value = .201

Since the p-value for water and sun are both less than .05, this tells us that both factors have a statistically significant effect on plant height.

And since the p-value for the interaction effect (.201) is not less than .05, this tells us that there is no significant interaction effect between sunlight exposure and watering frequency.

**Estimated Marginal Means**

The first table displays the means of the observations for each factor:

For example:

- The mean height of plants that were watered daily wasÂ
**5.893Â**inches. - The mean height of plants that received high sunlight exposure wasÂ
**6.62Â**inches. - The mean height of plants that were watered dailyÂ
*andÂ*received high sunlight exposure wasÂ**6.32Â**inches.

And so on.

**Post Hoc Tests**

This table displays the p-values for the Tukey post-hoc comparisons between the three different levels of sunlight exposure.

From the table we can see the p-values for the following comparisons:

- high vs. low: | p-value =Â
**0.000** - high vs. medium | p-value =Â
**0.000** - low vs. medium | p-value =Â
**0.447**

This tells us that there is a statistically significant difference between high and low sunlight exposure, along with high and medium sunlight exposure, but there is no significant difference between low and medium sunlight exposure.

**Step 3: Report the results.**

Lastly, we can report the results of the two-way ANOVA. Here is an example of how to do so:

A two-way ANOVA was performed to determine if watering frequency (daily vs. weekly) and sunlight exposure (low, medium, high) had a significant effect on plant growth. A total of 30 plants were used in the study.

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A two-way ANOVA revealed that watering frequency (p

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Plants that were watered daily experienced significantly higher growth than plants that were watered weekly.

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Further, Tukeyâ€™s test for multiple comparisons found that plants that received high sunlight exposure had significantly higher growth than plants that received medium and low sunlight exposure. However, there was no significant difference between plants that received medium and low sunlight exposure.

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There was also no statistically significant interaction effect between watering frequency and sunlight exposure.