# One-Way ANOVA - Interpreting the results

I'm tyring to better understand ANOVA. I did a simple one-way ANOVA, in R, as follows:

Year represents the year a student is in college (Freshman, Sophmore or Junior). Score represents their score on a test. Is the following interpretation correct:

Since the p-value of the ANOVA is .756, we can conclude there is no difference in the means of the three groups of the Year factor and Year does not significantly impact the mean Score.

This sounds correct to me but I'm a little unsure how to fully interpret one-way results.

• Randy, there is very good introduction to Practical Regression and ANOVA using R. It's free and worth a read as it may help you get started. Jan 3, 2017 at 21:15

in one way anova, the tested hypothesis is:

h0: b.Freshman = b.Sophmore = b.Junior = 0

h1: else

(b standing for the group coefficient)

so basically your result means that the variance between groups is small and hence cannot be a good explenation to the overall variance in the dataset.

generally ANOVA stands for analysis of variance. unlike regression models it does not try to estimate the coefficients, but rather give a simple answer to the question: "is there any significant difference between the groups". or in other words "how much of the total variance in the dataset can be explained by dividing the data into given groups?"

It is not valid to conclude the null hypothesis is true when the effect is not signicant. Better to say "No evidence was found for an effect of year." Sometimes it is better to say something like "There was a strong hint of an effect of Year but no conclusive evidence" when, for example, the p is 0.07 or so (this is the Fisher rather than the Neyman-Pearson approach).

Also, you never conclude the differences are significant. You calculate whether the differences are significant and significance is used to help you draw a conclusion (or not). Significance is a tool for drawing conclusions, not part of the conclusion itself.