Confused to interpret p-values Sorry, if question is meaningless but I have started to learn concept of P-value and confused to interpret that, if actual results are in favour of hypothesis but p-value are against it then what statistics we should go with?
For an example -
Let's say, I have two variables 'A' and 'B' then:
my null hypothesis says: Variable 'A' is greater than 'B' and
alternate hypothesis says: Variable 'A' is either less than or equal to Variable 'B'
Now, based on the test performed there would be two conditions:

*

*A=120 and B= 100, p-value= 0.02

Based on above result Variable A > Variable B but P-value is less than alpha i.e. 0.05 so can we still reject the null hypothesis that A > B?


*A=100 and B=110, P-value= 0.11

As, above says Variable A < Variable B but P-value is more than alpha i.e. 0.05 so can we accept null hypothesis that A > B ?

In your first example, you seem to have run a two-sided test that notices B being higher than A. However, you are interested in a one-sided test in the direction that turned out to be the opposite of what the data show. If you tweak your test to be one-sided, you will get a large p-value.
(The exact phrasing of your null and alternative hypotheses leave something to be desired, but how to phrase them based on your particular questions really warrants a separate question post.)
In your second example, the magnitude of difference is smaller than in the first example. Assuming the same sample sizes in both examples, the second example is going to return a larger p-value, due to the smaller magnitude of difference. However…

*

*We don’t accept null hypotheses.


*You posit that $A>B$, observe $B>A$ (opposite), and conclude that you were right. This is bizarre logic.
