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.

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#### Best Answer

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?"

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