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What does it mean if the F value in one-way ANOVA is less than 1? Remember the F-ratio is $$\frac{\sigma^2+\frac{r\times\sum_{i=1}^t \tau_i^2}{t-1}}{\sigma^2}$$

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute v...

This question is motivated by my question on meta-analysis. But I imagine that it would also be useful in teaching contexts where you want to create a dataset that exactly mirrors an existing publi...