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Suppose that there are $c$ pieces of candy total shared by $s$ students in the class. In group A, there are $.8\cdot s$ students sharing $.4\cdot c$ pieces of candy. Dividing the two, we have $\frac{.4c\text{ pieces of candy}}{.8s\text{ students}}$, or $.5\frac{c}{s}$ pieces of candy per student. In group B, there are $.2\cdot s$ students sharing $.6\cdot c$ pieces of candy. Dividing the two, we have $\frac{.6c\text{ pieces of candy}}{.2s\text{ students}}$, or $3\frac{c}{s}$ pieces of candy per student. The ratio between the pieces of candy per student in group A and that in group B is $\frac{.5\frac{c}{s}}{3\frac{c}{s}}=\boxed{\frac{1}{6}}$.