Interpret F-Value in ANOVA [duplicate]

When we conduct an ANOVA, we get F-Value and P-Value. If P-value if smaller than our alpha level of .05 for example, we reject our null hypothesis. What is the importance of F-Value that is obtained in the table as output? How it should be interpreted especially when conducting a within-subject ANOVA test? Thanks

• Possible duplicate here? -- and perhaps some relevant insight here Commented Feb 24, 2014 at 3:00
• well, why do we need to check the F-value; Does the p-value not tell us whether to reject or not to reject the null hypothesis? Commented Feb 24, 2014 at 3:16
• Why indeed? If you're comfortable with the p-value, the F is obtainable directly from it (taking the relevant degrees of freedom as a given) simply via the inverse cdf, so neither contains any information not in the other. However, some people may find the ratio of variances more readily interpretable than p-value (in the same way many people tend to find a t-statistic interpretable), others may use it out of little more than habit and convention. Commented Feb 24, 2014 at 4:38

One other issue to be aware of is the controversy regarding the Neyman–Pearson framework for interpreting significance statistics. There are alternatives to dichotomizing p values as less or greater than $\alpha$ for the sake of interpretation. IMO, one should have a better reason for not rejecting the null if
p = .051 (e.g., pragmatic, "real-world" costs or risks, or the ability to replicate), unless one really isn't all that interested in the alternative hypothesis in the first place. Many studies are more about effect size than about statistical significance anyway, so it would often be better to focus on effect sizes and present confidence intervals than to focus on null hypotheses, especially when statistical power is not the limiting factor in the study. For more on this, see "Is the exact value of a 'p-value' meaningless?" For a simple repeated measures ANOVA, consider interpreting $\eta^2$ (see here for an intro), especially if you have plenty of data.