Dogs like any other animal are intimidated by any other animal of superior size and strength.
This may seem a little odd when you consider the typical ankle biter but you must realize that small dogs are easily intimidated by just about everything out there thus they feel the need to do a little intimidation of their own.
I am sure nearly everyone can remember seeing a small dog go after a larger dog aggressively only to retreat as soon as the larger animal shows any sign of aggression.
Animals attempt to show dominance in what ever way they can, some ways are far more effective than others.
Owners of Great Danes often run into the problem of introducing their huge beasts to smaller dogs.
These small dogs most often go ballistic and make a bad situation worse by drawing attention to themselves.
A great dane was bread to chase and corner and it will often revert to its genetics when goaded into a chase.
From the perspective of a small dog it must be pretty terrifying to be chased by a beast that size and it unfortunately often leaves a lasting impression.
A home in which the animals do not get along can be a high strung stressful place.
All of this is avoidable by proper introductions.
First, both animals must be on leashes.
It is a good idea to exchange smells before they actually make acquaintance.
The smaller dog must be in a comfortable safe environment and must have a means by which to escape if it feels the need, not a real escape, just the illusion to increase the comfort level.
When first introductions are made the great dane must be firmly held and the smaller dog must be allowed to survey the situation, reward calm behavior with a treat and affection, make this a good experience.
Allow the smaller dog to approach the Dane, continue rewards and affection, continue firm grip on the Dane.
At this point observe both dogs behavior, look for submissive or playful behavior.
Head down tail up is good, wagging tail is always good, if the Dane wants to get down by all means encourage the big dog to get down and at least appear a little smaller.
If the Dane is salivating, Abort!!!, just kidding, I have never seen this happen.
Once you are comfortable with the situation allow the smaller animal to continue the approach and start the exploratory process.
All the while keeping the Dane in a calm submissive state.
Continue the rewards and affection on both sides of the aisle.
Remember you want this to be a good experience for both dogs, food and affection breeds great memories and associations in dogs.
Slowly move to remove leashes starting with the smaller dog and only removing the great danes leash when calm has been achieved.
Stay close and continue praise and reward until you are satisfied then let them romp.
This could be the start to a great friendship.