Data points that lay substantially beyond the range of this box and whisker plot were identified as potential outliers.
However, we would argue that doing this involves going substantially beyond the traditional focus of public health on simply identifying underlying causes, to developing the tools needed to understand these determinants as they manifest themselves across time and space.
Thomas S. Neuberger and Stephen J. Neuberger, father-son lawyers for the plaintiffs, say they have saved the most damning evidence for this phase, and that the award to the plaintiff could grow substantially beyond the compensatory damages.
But the risk of hitting quite a number of health problems, one might say, goes up substantially beyond the age of 70.
Yet she was unable on Tuesday to build her base of support substantially beyond the white, working-class voters who had sustained her for the last month.
Mr. Spitzer announced his resignation 11 days ago, after reports of something that was substantially beyond "the far end of the typical thing" — his involvement as a client of a high-priced prostitution ring.
Similarly, nobody should have expected the pope's words at Yad Vashem, the Holocaust memorial outside Jerusalem, to have gone substantially beyond the guarded apology for the church's historical anti-Semitic sins that he issued in a sermon two weeks ago.
Both G.M. and Ford are expected to report big profits for 2010 in the next few weeks, and earnings could grow substantially beyond that in a 13.5 million market.
For the first time, the Biennial extended substantially beyond the Whitney Museum of American Art's Madison Avenue confines to occupy many of the wood-paneled period rooms and other spaces inside the armory from March 6 through Sunday night (the Biennial exhibits at the Whitney itself remain on display through June 1).
Without correctness, sampling bias is introduced and sampling variation is increased, sometimes substantially, beyond the unavoidable statistical sampling variation.
