Si, cuando las pruebas de medias post hoc difieren en sus resultados, es debido a que el cuadrado medio del error, el cual no es lo suficientemente pequeño para darle sensibilidad a la prueba de medias. De todas las pruebas de medias post hoc las más sensible es la F de Fisher mejorada, en cambio la MDSH de Tukey es menos sensible. Para solucionar esta situación, se pueden utilizar contrastes ortogonales o contrastes de medias a priori. La otra vía, es si en el ANAVAR se observan diferencias de p

Hola Carlos, que bueno saber de ti. Muchas gracias por la aclaración, 

Saludos Manuel, disculpa que no te respondí en inglés, pero me salió muy larga la recomendación. Un abrazo cordial

look at post:

https://www.researchgate.net/post/Has_anyone_ever_had_an_ANOVA_with_P00001_and_with_no_difference_between_means_by_Tukey_test

It is possible for an ANOVA test to be significant while the post hoc test is not significant. If the Tukey test was not significant, try another post hoc test like Duncan multiple range test. Duncan test is known to be very powerful. The t test may not be appropriate in this circumstance because very many such tests may be necessary since it is pairwise..

 Dear Manuel,

When ANOVA (as an omnibus statistical test) is showing Fexp (treatment/s and experimental error ratio) with p less than 0.05 (or other value you define) it means that at least two arithmetic means are, statistically, significantly different.

That case indicate that these treatments or factors are not from the same set, sample or population. However, to perform any type of anova  (single factor, two-way, three-way etc) same assumptions should be considered (normality, symmetry,homogeneity of variances, interval data of the dependent variable, absence of multicollinearity, outliers etc.) so you should perform Hartley-test, Chi square etc and check skewness and kurtosis of distribution. Most important is to check your coefficients of variation, which should be app. 5-30%.

If these assumptions are not considered, your results will be hard to discuss. Post-hoc tests differ by their sensitivity (the size of the difference between treatments to detect), but any test you use it should show at least one difference between one pair of arithmetic means if assumptions are fulfilled.

The selection of post-hoc tests (as well as the performing the ANOVA) depends on your previous research, characheristics of variables, experimental design, and sensitivity and objectivity you want to achieve. T-test statistics is ANOVA statistics, so t equals to square of F. Lsd-test is actually a t-test with single standard error for all arithmetic means (factors, treatments).

Thank for your comments everyone, I have expanded my vision on this topic

Fisher designed the least significant difference test (LSD) as a follow up.  Alpha was not adjusted so it is guaranteed to find which two means differ.  Remember, however, Fisher only made categorical statements (this mean is different than that mean) rather than measurement statements.