Sense of place can be a deep personal connection. However through experience and physical changes ones sense of a place can also be changed. How can this change be measured?
Sense of place, maybe it is related to placemaking. In that context, a good method to "measure" (although sense of place doesn't work in and objective world and can't be measured) will be an ethnographic approach. May be you could read Sarah Pink "Doing Sensory Ethnography" from Routledge.
As it is a very subjective issue, I think that the best tool is the personal interview. "The Image of the City" by Kevin Lynch is a useful book about that.
Sense of place depends on general effects, such as environment, society, customs and traditions. On the other hand, it depends on personal effects such as personal and psychological history, personal experiences. So you can't access to accurate results. In this case survey would be possible to reach the most / least percentage ratio. It's just like asking " what is the most favored color between people ?".
Sense of place is a very complex and interdisciplinary concept. till the current day, there is no one definition that shares consensus from all related disciplines. disciplines involve: social psychology, social anthropology, environmental psychology, human geography, urban and architecture theories ... not to mention lack of consensus on methods of measuring. there is no agreement even on its typologies.
what is relatively agreed upon is that:
places are the product of people coming into space
perception of places differs according to a lot of things, including a person's background, his/her values, culture, social group, other social groups in space, activity, ... other aspects related to the area of study.
on the other hand, there are the discussion about "powerful atmospheres" - what lynch calls Imageability: the ability of the physical setting to provoke meaning in any given user.
A lot of studies discussed what makes influential spaces. - but you never define one kind of meaning or impression which would be provoked by the space - you never know what would a random person think of what you think is obvious. ex. a Chair can is typically used for sitting but someone can hang it on a wall and use it as a shelf another will sleep on it. this is the phenomenology of place.
The term sense of place focuses on subjective quality, which links physical experiences with imaginative constructions.
Sense of place is: (a) “Creating somewhere that is recognizably distinct, but simultaneously strengthens local identity” (Carmona et al., 2003, p. 33); (b) “Making connections is an essential part of creating a sense of place. This means that roads, streets and the routes for utilities should be designed in response to the local context” (Carmona et al., 2003, p. 69).