Compare a concept in The New Negro to a concept in "Sweat" by Zora Neale Hurston.

It is important to know that the ideas presented by Alain Locke in The New Negro, his study of the Harlem Renaissance, and those presented by Zora Neale Hurston, particularly in "Sweat," are somewhat at odds with each other. Locke and Hurston also had an ideological disagreement that was made public. Locke thought that Hurston wrote literature that negatively represented black people. Hurston countered by accusing Locke of inauthenticity.
The New Negro describes the political, cultural, economic, and social development of black people in the 1920s. This development was the result of multiple factors, including The Great Migration—the mass movement of black people from the South to the major cities of the Northeast and the Mid-West—as well as white patronage of black art and literature. The "New Negro" was self-aware, self-defined (supposedly), more economically and socially mobile, and had the means to express him- or herself in artwork that was distinctly "black." The "New Negro" existed in a world that was sophisticated, cosmopolitan, and hopeful.
The rural Floridian world in which Hurston's characters exist in "Sweat" is the polar opposite. Delia is an abused wife who makes a living by washing the clothes of white families. Her suffering ends when her husband, who is foolish enough to think that he can control nature simply because he controls her, is killed by his own hubris.
The concept that both the story and Locke's notion of "the New Negro" have in common is that of transformation. Locke described a "younger generation . . . vibrant with a new psychology" and a "new spirit awake in the masses." The "Old Negro" was a problem to be solved, "something to be argued about, condemned or defended, to be 'kept down,' or 'in his place,' or 'helped up,' to be worried with or worried over . . ."
Delia's condition is similar. The men in her community commiserate over her mistreatment at the hands of her husband, Sykes, who debases her thin body and threatens to displace her in her own home. However, Delia—who is the sole earner in the household due to her work as a washerwoman—refuses to accept Sykes's insults and condemns his maltreatment: 

"Delia pushed back her plate and got up from the table. 'Ah hates you, Sykes,' she said calmly. 'Ah hates you tuh de same degree dat Ah useter love yuh. Ah done took an' took till mah belly is full up tuh mah neck. Dat's de reason Ah got mah letter fum de church an' moved mah membership tuh Woodbridge—so Ah don't haf tuh take no sacrament wid yuh. Ah don't wantuh see yuh 'roun' me atall. Lay 'roun' wid dat 'oman all yuh wants tuh, but gwan 'way fum me an' mah house. Ah hates yuh lak uh suck-egg dog.'

Sykes is shocked by her response, expecting her to accept his abuse, just as the "Old Negro" might have accepted the abuse that coincided with white supremacy. Her rejection of continual suffering is not unlike the New Negro's rejection of Southern life in favor of improved conditions in the North. 
What is interesting about Hurston's construction of her characters is that they are rooted in their communities. Delia will not leave her home, despite Sykes's attempts to turn it into a site of fear. This is similar to the way in which Janie Starks, Hurston's protagonist in Their Eyes Were Watching God, never abandons her Florida home, in spite of her uncomfortable history there. Hurston did not seem to believe that a better life existed for black people somewhere else. They were offered a different life, but one in which they would encounter the same problems and encumbrances.
The New Negro, on the other hand, was migratory, traveling throughout the United States and, sometimes, across the Atlantic. Free movement was a key aspect of the New Negro's impulse toward self-determination. For Hurston, the right to claim one's own community, one's own home, reflected this self-determination. However, in both cases, this mode of thinking epitomized a new hope and a new sense of self that had emerged in the 1920s.