Report the result of the one-way ANOVA (e.g., "There were no statistically significant differences between group means as determined by one-way ANOVA (F(2,27) = 1.397, p = .15)"). Not achieving a statistically significant result does not mean you should not report group means ± standard deviation also. However, running a post hoc test is usually not warranted and should not be carried out.
Firstly, you need to report your results as highlighted in the "How do I report the results of a one-way ANOVA?" section on the previous page. You then need to follow-up the one-way ANOVA by running a post hoc test.
You need to perform the same procedures as in the above three sections, but add into your results section that this assumption was violated and you needed to run a Welch F test.
Recall from earlier that the ANOVA test tells you whether you have an overall difference between your groups, but it does not tell you which specific groups differed – post hoc tests do. Because post hoc tests are run to confirm where the differences occurred between groups, they should only be run when you have a shown an overall statistically significant difference in group means (i.e., a statistically significant one-way ANOVA result). Post hoc tests attempt to control the experimentwise error rate (usually alpha = 0.05) in the same manner that the one-way ANOVA is used instead of multiple t-tests. Post hoc tests are termed a posteriori tests; that is, performed after the event (the event in this case being a study).
There are a great number of different post hoc tests that you can use. However, you should only run one post hoc test – do not run multiple post hoc tests. For a one-way ANOVA, you will probably find that just two tests need to be considered. If your data met the assumption of homogeneity of variances, use Tukey's honestly significant difference (HSD) post hoc test. Note that if you use SPSS Statistics, Tukey's HSD test is simply referred to as "Tukey" in the post hoc multiple comparisons dialogue box). If your data did not meet the homogeneity of variances assumption, you should consider running the Games Howell post hoc test.
First off, it is not essential that you present your results in a graphical form. However, it can add a lot of clarity to your results. There are a few key points to producing a good graph. Firstly, you need to present error bars for each group mean. It is customary to use the standard deviation of each group, but standard error and confidence limits are also used in the literature. You should also make sure that the scale is appropriate for what you are measuring. Generally, if graphically presenting data from an ANOVA, we recommend using a bar chart with standard deviation bars.
Now that you understand the one-way ANOVA, you can go to our guide on how to run the test in SPSS Statistics here.