The ANOVA procedure tests these hypotheses:

Here's a typical piece of output from a single-factor analysis of variance.

Click on the Options button in the One-Way ANOVA dialog box.

To do a for a one-way anova is kind of tricky, because you need to decide what kind of effect size you're looking for. If you're mainly interested in the overall significance test, the sample size needed is a function of the standard deviation of the group means. Your estimate of the standard deviation of means that you're looking for may be based on a pilot experiment or published literature on similar experiments.

First consider the one-way ANOVA.

If the data show a lot of (different groups have different standard deviations), the one-way anova can yield an inaccurate P value; the probability of a false positive may be much higher than 5%. In that case, you should use Welch's anova. I've written a . It includes the Games-Howell test, which is similar to the for a regular anova. (Note: the original spreadsheet gave incorrect results for the Games-Howell test; it was corrected on April 28, 2015). You can do Welch's anova in SAS by adding a MEANS statement, the name of the nominal variable, and the word WELCH following a slash. Unfortunately, SAS does not do the Games-Howell post-hoc test. Here is the example SAS program from above, modified to do Welch's anova:

PROC GLM doesn't calculate the variance components for an anova. Instead, you use PROC VARCOMP. You set it up just like PROC GLM, with the addition of METHOD=TYPE1 (where "TYPE1" includes the numeral 1, not the letter el. The procedure has four different methods for estimating the variance components, and TYPE1 seems to be the same technique as the one I've described above. Here's how to do the one-way anova, including estimating the variance components, for the mussel shell example.

This is an important assumption made by the analysis of variance.

Analyzing the log-transformed data with one-way anova, the result is F6,76=11.72, P=2.9×10−9. So there is very significant variation in mean genome size among these seven taxonomic groups of crustaceans.

5 Requirements for One-way ANOVA 1.

Partitioning the variance applies only to a model II (random effects) one-way anova. It doesn't really tell you anything useful about the more common model I (fixed effects) one-way anova, although sometimes people like to report it (because they're proud of how much of the variance their groups "explain," I guess).

Statcrunch Guide for One-way ANOVA: 1.

There's an equation you can use for in experiments. It's usually used for nested anova, but you can use it for a one-way anova if the groups are random effect (model II).

Go to STAT and go to ANOVA and open up the One-way. 3.

Another area where partitioning variance components is useful is in designing experiments. For example, let's say you're planning a big experiment to test the effect of different drugs on calcium uptake in rat kidney cells. You want to know how many rats to use, and how many measurements to make on each rat, so you do a pilot experiment in which you measure calcium uptake on 6 rats, with 4 measurements per rat. You analyze the data with a one-way anova and look at the variance components. If a high percentage of the variation is among rats, that would tell you that there's a lot of variation from one rat to the next, but the measurements within one rat are pretty uniform. You could then design your big experiment to include a lot of rats for each drug treatment, but not very many measurements on each rat. Or you could do some more pilot experiments to try to figure out why there's so much rat-to-rat variation (maybe the rats are different ages, or some have eaten more recently than others, or some have exercised more) and try to control it. On the other hand, if the among-rat portion of the variance was low, that would tell you that the mean values for different rats were all about the same, while there was a lot of variation among the measurements on each rat. You could design your big experiment with fewer rats and more observations per rat, or you could try to figure out why there's so much variation among measurements and control it better.

One-way anova - Handbook of Biological Statistics

Although statisticians say that each level of an anova "explains" a proportion of the variation, this statistical jargon does not mean that you've found a biological cause-and-effect explanation. If you measure the number of ears of corn per stalk in 10 random locations in a field, analyze the data with a one-way anova, and say that the location "explains" 74.3% of the variation, you haven't really explained anything; you don't know whether some areas have higher yield because of different water content in the soil, different amounts of insect damage, different amounts of nutrients in the soil, or random attacks by a band of marauding corn bandits.