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
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2$\begingroup$ Possible duplicate here? -- and perhaps some relevant insight here $\endgroup$– Glen_bFeb 24, 2014 at 3:00
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$\begingroup$ 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? $\endgroup$– user39531Feb 24, 2014 at 3:16
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1$\begingroup$ 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. $\endgroup$– Glen_bFeb 24, 2014 at 4:38
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$\begingroup$ Dear user39531, you asked 21 questions on this site and got for 16 at least one answer. But your vote count shows only ONE up vote and nothing else. Moreover, no answer has ever been accepted by you. Accepted answers and up votes are, however, sort of the daily meal for people offering their time in order to help people which only contribute by questions - people like you. Please appreciate answers with votes, accept them and make us smile. $\endgroup$– random_guyJan 10, 2015 at 19:10
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2 Answers
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As @Glen_b noted, F is a ratio of variances. If there's an advantage to interpreting it instead of p, it's that you don't need to convert it to F to obtain that ratio, if that's what you want to interpret. This is a somewhat circular answer, but since both are functions of one another, there's not much more to say.
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.
answered Jun 1, 2014 at 20:20
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You can compare the calculated F value and the tabulated F value. If the calculated is less the tabulated at the given alpha value you accept the null hypothesis otherwise you reject. So, you have the liberty of either using the F value or the p value. But if you are doing you calculation manually using F value is more simpler, if you are using a software then p-value is simpler.
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$\begingroup$ Thanks, that helps. I thought that F-Value gave us some additional info that p-value would not. That clarifies my doubt now. $\endgroup$ Feb 24, 2014 at 17:40