Do measures of Big 5 personality have a positive bias towards extraverted, conscientious, emotionally stable, ageeable and open individuals?
Backstrom et al (2009) have a paper devoted to the question of whether the intercorrelations between the Big 5 scales is due to social desirability bias or substantive factors.
In Study 2 they re-wrote each item on a 100 item IPIP scale so that each item had reduced positive bias. They then administered the original and neutrally worded items to a sample of participants. They found that when IPIP items were worded in a more evaluatively neutral fashion, the correlations between the Big 5 were substantially reduced. Specifically, they state that:


  The first component accounted for 19.3% of the variance in the IPIP
  items as compared with the variance of the first component from the
  analysis of the neutral items of 10.5%. The mean correlation between
  the first principal component and the items was .40 for the IPIP items
  and .12 for the neutral items.


Their first paragraph in the discussion captures several interesting conclusions:


  Taken together, the two studies presented here support a model that
  still appears to be controversial. The model can be described as
  follows: when we use self-ratings for the measurement of personality
  traits, some items tend to activate social desirability concerns. In
  the scores, the participants’ tendency to respond in a socially
  desirable way is mixed with the descriptive aspect of the items, which
  is supposed to measure the FFM. The result is a common factor related
  to all of the other factors in the inventory (Edwards and Edwards,
  1991 and Peabody and Goldberg, 1989). It has been shown several times
  that this factor can be reduced, and that when this is done the items’
  descriptive quality stands out more clearly. In previous studies the
  social desirability of the items has been reduced by simply selecting
  items that correlate weakly with social desirability inventories (e.g.
  Jackson et al., 1996). In the present study, the focus was on the
  semantic content of the items. By systematically making the items from
  the IPIP-100 less attractive, without changing their meaning in any
  crucial way, we could get rid of almost all common variation between
  the factors, i.e. variation related to social desirability. These new
  items appeared to measure the same thing as the original items in the
  IPIP-100, except social desirability. This shows that it is relatively
  easy to create personality inventory items that measure FFM traits
  with less influence of social desirability. We therefore encourage
  inventory constructors to henceforth strive for making inventories
  where descriptive scales are less confounded with social desirability.


References


Bäckström, M., Björklund, F., &amp; Larsson, M. R. (2009). Five-factor inventories have a major general factor related to social desirability which can be reduced by framing items neutrally. Journal of Research in Personality, 43(3), 335-344. PDF