05, we reject the null hypothesis of the ANOVA and conclude that there is a statistically significant difference between the means of the three groups. To find the p-value that corresponds to this F-value, we can use an F Distribution Calculator with numerator degrees of freedom = df Treatment and denominator degrees of freedom = df Error.įor example, the p-value that corresponds to an F-value of 2.358, numerator df = 2, and denominator df = 27 is 0.1138.
To determine if the difference between group means is statistically significant, we can look at the p-value that corresponds to the F-statistic. Thus, the larger the F-statistic, the greater the evidence that there is a difference between the group means. The larger the F-statistic, the greater the variation between sample means relative to the variation within the samples. F-statistic: Variation between sample means / Variation within samples.F-statistic: Mean Squares Treatment / Mean Squares Error.The F-statistic is the ratio of the mean squares treatment to the mean squares error: Two values that we immediately analyze in the table are the F-statistic and the corresponding p-value. Whenever you perform an ANOVA, you will end up with a summary table that looks like the following: Source H A: At least one group mean is different from the rest.An ANOVA (“analysis of variance”) is used to determine whether or not the means of three or more independent groups are equal.Īn ANOVA uses the following null and alternative hypotheses:
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