The larger the variance (σ²), the lower the power. In the formula for z:

increasing σ² increases the denominator and therefore lowers z and power. For the example, σ is the standard deviation of the difference scores. The power of the test using the .05 significance level, for N = 25, µ

σ |
Power |

50 75 100 125 150 |
0.52
0.26 0.17 0.12 0.10 |

There are ways that an experimenter can reduce variance to increase power. One is to define a relatively homogeneous population. For instance, if one were studying reading speed, one could begin by studying the population of people in their first year at a selective college rather than the population of all English-speaking adults. The variance would be much reduced.