Again - strictly speaking - the assumed correspondence in (conventional) science is two-way.
From one perspective we can maintain that object phenomena (quantitative) are unaffected through relationship to the mental constructs which give them organisation (qualitative).
So someone testing a hypothesis will typically believe that the phenomena under investigation remain unchanged through relationship to this hypothesis. (Interestingly however, though this assumption breaks down at the level of quantum reality, scientists are still reluctant to accept that this points to a fundamental problem of interpretation that - strictly speaking - equally applies to the ordinary macro level).
However from the other perspective, we can maintain that mental hypotheses (qualitative) are unaffected through relationship to observed physical phenomena (quantitative).
Now of course scientists will accept that observations may well test the validity of a hypothesis (though not its actual nature).
So though - from this perspective - the views on the value of a hypothesis may well change following phenomenal observations, the actual hypothesis will still remain the same.
However once we accept the dynamic interaction of polar opposites in experience, then any strict correspondence as between theories (qualitative) and observations (quantitative) either of a deductive or inductive kind are no longer strictly tenable.
The resolution therefore of the resulting problems comes - not at the level where poles are separated - but rather at the levels where they are gradually reconciled.
Integral science is the story of this dynamic reconciliation.