I'm not very good in statistics. But recently for an ANOVA test I conducted in excel, I got a extremely high F value compared to F-crit. Like, F-value was in 3 digits whereas F-crit was only around 2.34.
Of course, since F-value is higher than F-crit, and p-value is lower than 0.05, I could interpret that means of the groups are statistically significant. But, I'm quite concerned as to why the F-value would be extremely higher than F-crit. None of the examples I saw in the internet had such a huge difference between those two values. What are the reasons for such a huge difference?
Is it completely normal to have such a huge value or is it wrong and there's a chance that I might have made a mistake? OR, do such huge differences in these values mean that ANOVA may not be the appropriate test for the data?
Thanks in advance
In the context of one-way ANOVA, the $F$ statistic is given by $$F=\frac{MS_b}{MS_w}$$ where $MS_b$ measures the variance between group sample means and $MS_w$ measures the variances within each group. An extremely high $F$ statistic implies that $MS_b>>MS_w$ (the variance between group means is very large compared to the variance within each group). To put it simple, the values within each group do not differ significantly from one another, while those across different groups do. This suggests unequal means across groups, so in the case of an extremely high $F$ statistic we reject the null hypothesis of equal means between groups.