Allelopathic Effects on Root and Shoot Growth:
One-Way Analysis of Variance (ANOVA) in SPSS
Dan Flynn
Just as t-tests are useful for asking whether the means of two groups are different, analysis of
variance (affectionately known as ANOVA) can answer the question of whether the means of
many groups differ from each other. Biologists find ANOVA useful because we often design
experiments with many treatments (such as different drugs), and then want to know whether
some variable (such as the proliferation of cancer cells) is different between experimental
groups.
Preparing the Data
In this example, we will look at the allelopathy data you collected. There are a few details about
working with SPSS that require reformatting the data, before starting the analysis. In Excel, open
classSEEDdata.xls, and add a worksheet for each of the target species (lettuce, rye, and radish).
SPSS needs the data to be in “long” format, meaning each row is a separate experimental unit (a
seed in this case). The final format will look like this:
The easiest way to do this is just to cut and paste your data (and use Edit > Fill > Down in
Excel). One important point is that SPSS needs to have the treatment groups be labeled with
numbers, not letters (in SPSS, this is called a numeric explanatory variable, as opposed to a
“string”). The “Code” variable specifies the species of herb you tested.
Now open up the data for one of the target species (like lettuce) in SPSS. Notice the tab on the
bottom of the window, called “Variable View”. Click that and you can see how SPSS is treating
each of the columns in the data set.
ANOVA in SPSS
Barnard College – Biological Sciences
Click on “Code” and enter labels in the Values box to make the results easier to interpret. This
will make the actual names, rather than the numeric values, show up in the analysis results.
Running ANOVA in SPSS
Now that the data are ready, you can begin the ANOVA. Go to Analyze > Compare Means >
One-way ANOVA.
Select the variable you want to look at and put it in the Dependent List. You can choose more
than one variable to analyze, both root and shoot for example. The Factor is your independent
variable, which will define the groups to compare.
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ANOVA in SPSS
Barnard College – Biological Sciences
Note: There is only one variable allowed in the Factor box; this is what is meant by a
"one-way" ANOVA, since we are looking at how a single categorical variable explains
the variance in a continuous variable.
Reading the Output
The SPSS output for ANOVA is detailed, but the main results are fairly concise. The last column
of the ANOVA table is the significance value, or the p-value: if it is below 0.05, we can reject
the null hypothesis that there is no difference between the group means; if p < 0.05, we can say
that there is a significant difference between means. [The literal meaning of any p-value of 0.05
is that if we repeated the experiment 100 times, in only 5 of the 100 tests would we observe a
result like the one we just saw by chance alone. So it is not the same as saying we are 95% sure
the result differs from the null hypothesis.]
ANOVA
Shoot
Sum of
Squares
df
Mean Square
Between Groups
4004.541
4
1001.135
Within Groups
7275.896
245
29.698
11280.438
249
Total
F
Sig.
33.711
.000
A cleaned-up version that gives the most important information would look like this:
df
Seed treatment
Residuals
Sum of Squares
Mean Square
4
4004.5
1001.1
245
7275.9
29.7
F
33.7
p
<0.001
Note that the "within groups" line can be renamed "residuals." It represents the amount of
variation not explained by the treatment, which can be renamed here as "Seed treatment".
Now that we know that there is an overall difference across all three groups, we want to know
exactly what the difference is. In order to do this, we go through the steps to re-do the ANOVA.
Only this time, in the "One-way ANOVA" window select the “Post Hoc” button. Post hoc means
“after this” in Latin, and refers to tests we do after the fact to see how, knowing that the main
effect is significant, each treatment level relates to the others. If the main effect is not significant,
post hoc tests are not useful.
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ANOVA in SPSS
Barnard College – Biological Sciences
In the post hoc window, select Tukey (for Tukey's honestly significant difference, HSD) and
click “Continue” and then “OK”. Notice that there are lots of different tests we could choose
from, and they may give you slightly different values.
The resulting table takes some time to interpret just the first part of the table is reproduced
below. The table shows that lettuce seeds grown in the control treatment had significantly greater
shoot growth than those grown with rosemary and cilantro, and significantly less than those
grown with sage. Seeds grown with oregano did not differ from the controls.
Multiple Comparisons
Shoot
Tukey HSD
95% Confidence Interval
(I) Code (J) Code
Control
Mean Difference
Std. Error
(I-J)
Sig.
Lower Bound Upper Bound
Oregano
-1.8020
1.0899
.465
-4.797
1.193
Rosemary
6.4480*
1.0899
.000
3.453
9.443
Cilantro
5.4400*
1.0899
.000
2.445
8.435
*
1.0899
.007
-6.709
-.719
Sage
-3.7140
*. The mean difference is significant at the 0.05 level.
Note: If your table has cells filled with “*******”, this means that there are too many
digits for SPSS to display. You can double-click the chart to make it editable, and then
drag columns wider to make the values visible.
You would not report this table in your results, but use it to interpret the main result. It will be
much easier to do this while looking at a graph of the results, explained below.
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ANOVA in SPSS
Barnard College – Biological Sciences
Graphing Your Data with Bar Charts
Whenever comparing groups of cases by some single continuous variable, bar charts are
preferred. This is true for cases where you did a t-test to compare two groups, or where you did
an ANOVA to compare three or more groups.
The easiest way to make this graph is in Graphs > Chart Builder.
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ANOVA in SPSS
Barnard College – Biological Sciences
For a one-way ANOVA, you want to use the simple bar chart, the first option. Drag the
appropriate variables to the x and y axes. To add error bars, click "Display error bars" in the
Element Properties window and set it to 1 standard error.
You can edit it to change the labels, fonts, colors, and line widths by double-clicking the chart in
the Output viewer. For example, you can set the background color and box color to white for a
cleaner graph (as below).
To make a box plot, which shows more information about how the data are distributed within
each treatment group, go back to the Chart Builder and select the simple Boxplot option. Box
plots show the median as a horizontal line in the middle, the 25th and 75th percentiles as edges of
the box, and the 5th and 95th percentiles as the "whiskers". Any points beyond these values are
shown as points.
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