Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS. Dan Flynn

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1 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.

2 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. 2

3 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.] Shoot ANOVA Sum of Squares df Mean Square F Sig. Between Groups Within Groups Total A cleaned-up version that gives the most important information would look like this: df Sum of Squares Mean Square F p Seed treatment <0.001 Residuals 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. 3

4 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. Shoot Tukey HSD (I) Code (J) Code Control Multiple Comparisons 95% Confidence Interval Mean Difference (I-J) Std. Error Sig. Lower Bound Upper Bound Oregano Rosemary * Cilantro * Sage * *. 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. 4

5 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. 5

6 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 25 th and 75 th percentiles as edges of the box, and the 5 th and 95 th percentiles as the "whiskers". Any points beyond these values are shown as points. 6