I have the anova table like this and the question is asking me to find the p-value using R or otherwise, can someone help me with this? I'm totally struggling with this question.
Solved – find p-value using R with a ANOVA table
anovap-valuer
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I'm a bit confused by your question, but as you are planning on reporting both within- and between-subjects effects, I assume you are actually conducting a mixed-design ANOVA.
Regardless, the tables of descriptives are what you probably want to report; the estimated marginal means are the means controlling for covariates (i.e., the mean of X when Y is held constant at its mean value). How you report these depends on how many descriptives you have to report; I would report the means and standard deviations in text if there are only a few of them, and in a table if there are many.
For age, $F=1.0812=\frac{MS_\text{age}}{MS_\text{Residuals}}$. The same is true of the other $F$ values replacing age with weight or protein. This partials out the variance in carb that is related to the other two factors not being tested directly by the $F$ test in question, whereas using $MS_\text{Residuals}$ from a single-factor GLM in the denominator would not. Thus the hypothesis test is of whether the residual variance in carb that is not explained by your other factors can be explained by your given factor. More specifically, the $p$ value represents the probability that this residual variance would relate to your given factor at least as much as it does in your sample if you were to sample again randomly from a population in which the null hypothesis of no relationship between those residuals and your factor is literally true. As for why 16 and not 18, remember that controlling for these other factors costs you degrees of freedom: one apiece.
To elaborate in response to your edit/comment, another way of looking at your $F=3.5821$ is as $F=\frac{MS_\text{weight}}{MS_\text{Residuals}}$ for a general linear model with only one factor (weight). With that one-factor GLM's ${MS_\text{Residuals}}$ instead of a three-factor GLM's ${MS_\text{Residuals}}$ as the denominator (because you're not controlling for anything, hence what would've been the residuals are the observations $-\ \mu_\text{carb}$ instead, $\mu_\text{carb}$ being the intercept of the null model), you haven't partialed out any of the variance that weight can't explain but age or protein can, so the effect of weight appears less clear by itself.
When you control for the effects of age and protein, you reduce the amount of variance that still needs explaining in your model. This makes the predictive job a little easier for weight, because it no longer has to contend with the independent effects of age or protein in explaining carb. In a post hoc / retrospective sense, you can look back and say, "Well, no wonder weight didn't predict these observations as well by itself; age and protein vary in my sample too, and their independent effects were mucking things up for poor ol' weight!" Of course, these results are even better in an epistemic, hypothesis-testing sense if you expected in advance that this would happen, and chose multiple regression to examine hypotheses of independent effects you also specified in advance.
Best Answer
It should be as follows:
1-pf(171.5410/13.3074, 2, 325)You get your F statistic from the ratio of
MS-GroupandMS-Error. Plugging in the degrees of freedom for numerator and denominator (i.e. 2 and 325 respectively) into F distribution, we get p-value as:In other words, difference among means is statistically significant.