Intuitively interpreting the F-statistics in ANOVA I am trying to get the intuition of the definition of F-statistics in ANOVA. F is defined as MST(T for treatments)/MSE(E for error). So I thought that if there is no treatment effect then F should be 0, not 1. However, the answer seems to be 1. 
Please help me out with this and let me know if there is anything I am missing.
 A: The F statistic is computed as a ratio of two quantities, so it makes sense that 1 would be the reference point used to judge its magnitude.
If the F-statistic is much larger than 1, then MST is much larger than MSE, meaning there is more variability in the data due to the treatments than due to the other (unobserved or unaccounted for) factors. In other words, the signal (treatments) dominates the noise (unobserved or unaccounted for factors). This would provide evidence in favour of a treatment effect. 
If the F-statistic is hovering around 1, then MST is hovering around MSE. This would suggest no evidence in favour of a treatment effect. The signal (if it exists) is drowned by the noise OR there is no signal to begin with.
A: Well, for it to be zero, the MST(treatment) should be zero, implying that the means are exactly equal. You do not require that much. You would declare the treatment effect non significant if its size "can be expected" given the dispersion of the data values. The F statistic is thus kind of a signal-to-noise ratio, with high values leading to the rejection of the hypothesis $H_0$ .
A: No ratio can be 0 unless the numerator is 0 (a 0 denominator is undefined). Furthermore, note that F ratios are a ratio of variances, and variances also can’t be 0. 
Now the intuition is this: the F distribution quantifies the distribution of variance ratios. In ANOVA this is between groups (experimental variance) / within groups (error variance). If you have no treatment effect (or a weak one) you are left with only error in the numerator and denominator, yielding 1.0, or sometimes < 1.  Only if your treatment is effective will you get a ratio > 1.0
