The chi-square$\chi^2$ and F tests are one sided tests because we never have negative values of chi-square$\chi^2$ and F. For chi-square$\chi^2$, the sum of the difference of observed and expected squared is divided by the expected ( a proportion), thus chi-square is always a positive number or it may be close to zero on the right side when there is no difference. Thus, this test is always a right sided one-sided test. The explanation for F test is similar.
For the F test, we compare between group variance to sum of within group variances ( mean square error to SSw/dfw)$\frac{SSw}{dfw}$. If the between and within mean sum of squares are equal we get an F value of 1.Since
Since it is essentially the ratio of sum of squares, the value never becomes a negative number. Thus, we don't have a left sided test and F test is always a right sided one sided test. Check the figures of chi-square$\chi^2$ and F distributions, they are always positive.For both tests, you are looking at whether the calculated statistic lies to the right of the critical value. Daniel T. Dibaba