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BASICS DATA ANALYSIS T-TEST ANOVA CHI-SQUARE TEST

SPSS One-Way ANOVA Tutorial

For reading up on some basics, see ANOVA - What Is It?

ANOVA Example - Effect of Fertilizers on Plants

A farmer wants to know which fertilizer is best for his parsley plants. So he tries different fertilizers on different plants and weighs these plants after 6 weeks. The data -partly shown below- are in parsley.sav.

Screenshot of Data View Parsley Plant Experiment

Quick Data Check - Split Histograms

After opening our data in SPSS, let's first see what they basically look like. A quick way for doing so is inspecting a histogram of weights for each fertilizer separately. The screenshot below guides you through.

SPSS One Way ANOVA Split Histogram Dialog

After following these steps, clicking Paste results in the syntax below. Let's run it.

* Run split histograms.

GRAPH
/HISTOGRAM=grams
/PANEL COLVAR=fertilizer COLOP=CROSS.

Result

SPSS One Way ANOVA Split Histogram

Importantly, these distributions look plausible and we don't see any outliers: our data seem correct to begin with -not always the case with real-world data!
Conclusion: the vast majority of weights are between some 40 and 65 grams and they seem reasonably normally distributed.

Inspecting Sample Sizes and Means

Precisely how did the fertilizers affect the plants? Let's compare some descriptive statistics for fertilizers separately. The quickest way is using MEANS which we could paste from Analyze SPSS Menu Arrow Compare Means SPSS Menu Arrow Means but just typing the syntax may be just as easy.

*Basic descriptives table for grams by fertilizer.

means grams by fertilizer
/cells count mean stddev.

Result

SPSS One Way ANOVA Means Table

Now, this table tells us a lot about our samples of plants. But what do our sample means say about the population means? Can we say anything about the effects of fertilizers on all (future) plants? We'll try to do so by refuting the statement that all fertilizers perform equally: our null hypothesis.

One-Way ANOVA - Null Hypothesis

The null hypothesis for ANOVA is that all population means are equal. If this is true, then our sample means will probably differ a bit anyway. However, very different sample means contradict the hypothesis that the population means are equal. In this case, we may conclude that this null hypothesis probably wasn't true after all.
ANOVA will basically tells us to what extent our null hypothesis is credible. However, it requires some assumptions regarding our data.

ANOVA Assumptions

So how to check if we meet these assumptions? And what to do if we violate them? The simple flowchart below guides us through.

SPSS ANOVA Flowchart

SPSS One Way ANOVA Flowchart

So what about our data?

So why do we inspect our sample sizes based on a means table? Why didn't we just look at the frequency distribution for fertilizer? Well, our ANOVA uses only cases without missing values on our dependent variable. And our means table shows precisely those.
A second reason is that we need to report the means and standard deviations per group. And the means table gives us precisely the statistics we want in the order we want them.

SPSS One-Way ANOVA Dialog

We'll now run a basic ANOVA from the menu. The screenshot below guides you through.

SPSS One Way ANOVA Dialog 1

The Paste button creates the syntax below.

One-Way ANOVA Syntax

*Basic one-way ANOVA syntax.

ONEWAY grams BY fertilizer
/MISSING ANALYSIS.

SPSS One-Way ANOVA Output

SPSS One Way ANOVA Output

A general rule of thumb is that we reject the null hypothesis if “Sig.” or p < 0.05 which is the case here. So we reject the null hypothesis that all population means are equal.
Conclusion: different fertilizers perform differently. The differences between our mean weights -ranging from 51 to 57 grams- are statistically significant.

ANOVA - APA Reporting Guidelines

First and foremost, we'll report our means table. Regarding the significance test, the APA suggests we report

like so: “our three fertilizer conditions resulted in different mean weights for the parsley plants, F(2,87) = 3.7, p = .028.”

One-Way ANOVA - Next Steps

For this example, there's 2 more things we could take a look at:

ANOVA with Eta-Squared from MEANS

*ANOVA from MEANS includes eta-squared but not Levene's test or power estimates.

means grams by fertilizer
/statistics anova.

Result

ANOVA - Eta Squared Output from MEANS

Right, so that's about the most basic SPSS ANOVA tutorial I could come up with. I hope you found it helpful. Let me know what you think by throwing me a comment below.

Thanks for reading!

Previous tutorial: ANOVA – Simple Introduction

Next tutorial: SPSS One-Way ANOVA with Post Hoc Tests Tutorial

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