I know t-test works on mean differences, whereas F-test see variance.F-test is recommended when more than two groups are involved. But I wonder, will F-test be appropriate in situation where only two groups are there? When should one apply F-test or t-test where comparison between two groups has to be made? I have also seen that where t-test does not suggest any significant mean difference F-test shows significance, even in the situation of equal means.
If by F-test, you mean a standard analysis of variance, then, yes, it is fine to use with two groups. I believe the p-value for a one-way anova with two groups should be be the same as for Student's t-test. Likewise, Welch's anova should produce the same p-value as Welch's t-test.
with two groups, the clear (forementioned) algebraical relationship between t and F coming from the analysis of variance makes the two tests quite interchangeable for inference on the comparison of two means. however, if your p-value is borderline it may happen that you just exceed your preset confidence level with one method but not with the other. in such cases i'd take conflicting results as a warning and try to get more /new evidence before concluding that the two means are truly different.
J. Wilhelm's points are all important. Note that F and t give the identical p-value for the two-means comparison, provided that in the t test, you assume equal variances. If you use separate variance estimates in the t test, the p-values may differ from the F (which always assumes homoscedasticity), but usually not by much.
You have to check your results, steps in calculations and then if more than 2 groups use ANOVA.
t test for comparing means of two groups when parametric conditions are satisfied. If not you can use Mann Whitney U test . F test is for comparing means of More than two groups which satisfies parametric conditions.
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