Nose shape is not related at all to "race" or
ethnicity, but to region of origin. In today's world we are such a
mixed population that it's easier to go by race than where a population
originated.



It is a physical adaption which prevailed because people who had such features survived better.



Extreme cold favors flat faces with fat pads over the sinuses, and
narrow noses. These adaptations provide minimum surface area in
relation to body mass for minimum heat loss and protect the lungs and
base of the brain against cold air in the nasal passages. In conditions
of humid heat, where body heat must be dissipated, selection favours a
wide nose which prevents warming of the air in the nasal passages.



All noses inbetween are representative of which of these extremes you
are closer to. People's from the Middle East, and Africa, will have
large wide noses (not all, as there are small variations within
populations). Most of these people are African (black), Middle Eastern,
ect.. which leads to the racial remark that they have such large noses.
African groups and some Middle Eastern groups are considered to portray
"negroid" characteristics, this nose is even one of the characteristics
used by forensic anthropologists to identify that the skull was made by
an individual of that population (broad, long nasal cavity, with a
higher nasal bone)



People's in the arctic (Inuit) regions, or high altitude regions,
generally have flatter faces, and thus noses, more common of Asian
ancestry )because these are the migratory populations which founded
such populations). Many American Indian tribes and Central and South
American groups also portray these characteristics as their founding
populations were most likely Asian (or were at minimum mostly Asian,
many native Peruvians (not interbred with the Spainards) look very much
like eskimos because of this). Asian populations are known as
mongoloid, and a small flat nose is a trait which is even evident on
their bony remains (skulls).



Now we come to your more common "white" people, persons of European
decent (generally). Who tend to have smaller, narrow noses, which are
higher off the face than "mongoloid" noses. But the noses are narrower
than negroid populations. This is because it is an adaption between the
2 extremes. Europe experiences both cold winters and warm summers, so
an adaption in between negroid and mongoloid is needed. These Euro
populations are considered caucasian.



Within these you get variations. For instance Italians have noses more
like Africans, but Swedes and Icelandics have noses more like Asians.
Italy is more hot and humid than Sweden which is drier and colder.
People in India are a mix between negroid and mongoloid features.
People in Siberia have a mix of mongoloid and caucasian features.



It has nothing to do with race, but where the population of origin
adapted. These are always on a continueum, and this is why no single
characteristic can define a population or ethnic group.